MODE 5 3 on a Casio Calculator: Solve Quadratics (and Every MODE Menu Explained)

MODE 5 3 is the key sequence that opens the quadratic equation solver on Casio fx-991ES PLUS, fx-570ES PLUS and fx-115ES PLUS calculators (it is often written “MODE 53”, but it is three separate key presses). MODE opens the mode menu, 5 picks EQN (equation mode), and 3 picks aX² + bX + c = 0. Type a, b and c, pressing = after each one, then press = again to see the roots. To solve 2x² + x − 3 = 0, press MODE532=1=(−)3== and the calculator gives x = 1 and x = −3/2. No equation mode on your calculator, or no calculator at all? Type the equation into the free MathAI GPT math solver, or snap a photo of it with the iPhone app or Android app, and get the full working, not just the roots.

This guide covers every option in the Casio MODE menu, the equivalent keys on ClassWiz (fx-991EX) and older MS models, seven worked examples with a check for each, and the input mistakes that make the solver give a wrong answer. Key sequences follow Casio's own user's guides for the fx-570ES PLUS/fx-991ES PLUS, fx-115ES PLUS/fx-991ES PLUS C, fx-570EX/fx-991EX, fx-570CW/fx-991CW and fx-570MS/fx-991MS.

1) What the MODE key does

A Casio scientific calculator has several calculation modes. Each mode changes what the keys and the screen do: ordinary arithmetic, complex numbers, statistics, equations, matrices, and so on. The MODE key is how you switch between them, and the number you press next chooses the mode. On the fx-991ES PLUS, fx-570ES PLUS and fx-115ES PLUS the menu is:

Inside EQN mode (MODE5) a second menu asks which kind of equation you want:

So MODE 5 1 and MODE 5 2 solve systems of equations, MODE 5 3 solves quadratics and MODE 5 4 solves cubics. SHIFTMODE is different: it opens SETUP, where you pick Math or Line display, degrees or radians, and Fix/Sci rounding.

Watch out: the MODE key has nothing to do with the statistical mode (the most frequent value in a data set). For that, use the mode calculator or the guide to mean, median and mode.

2) MODE 5 3 step by step

1. Rearrange the equation so one side is 0 and the terms are in the order x², x, constant.
2. Read off a, b and c, including their signs. A missing term has coefficient 0.
3. Press MODE53. The coefficient editor shows columns a, b and c.
4. Type a, press =; type b, press =; type c, press =. Use the (−) key for negative numbers.
5. Press = to show the first root (X₁), and = again for X₂. The arrow keys scroll between them. Pressing = on the last root returns to the editor; AC also takes you back.
6. Check each root by substituting it into the original equation (section 5 shows how).

If an equation has one repeated root, the calculator shows a single X. If it has no real roots, the answers contain i (see Example 2). You can change one coefficient by moving the cursor to it, typing the new value and pressing =; AC in the editor resets all coefficients to zero.

3) The same thing on other Casio models

Only some Casio models number their menus this way. Find yours:

On a ClassWiz, “2” after Equation/Func means Polynomial and the second “2” is the degree, so a cubic is Polynomial then 3. The newer fx-570CW and fx-991CW have no numbered MODE menu: press HOME, select the Equation app icon and press OK, select Polynomial and press OK, then select ax²+bx+c and press OK to open the Coefficient Editor. Texas Instruments and Sharp calculators use completely different menus, so “MODE 5 3” does not apply to them.

4) Seven worked examples

Each example shows the keys, what the calculator returns, and the same problem worked by hand so you can see where the answer comes from. Key sequences are for the fx-570ES PLUS/fx-991ES PLUS.

Example 1: A quadratic that factors

Solve 2x² + x − 3 = 0. Here a = 2, b = 1, c = −3.

Keys: MODE532=1=(−)3==, then = for the second root.

Calculator: x = 1 and x = −3/2.

Example 2: No real roots (complex answers)

Solve x² + x + 3/4 = 0. Here a = 1, b = 1, c = 3/4.

Keys: MODE531=1=3÷4==

Calculator: x = −1/2 + (√2/2)i and x = −1/2 − (√2/2)i.

Example 3: Rearrange first, then MODE 5 3

Solve 3x² = 5x − 2. The most common mistake is typing a = 3, b = 5, c = −2 straight from this line.

Keys: MODE533=(−)5=2==

Calculator: x = 1 and x = 2/3.

Example 4: A word problem

A rectangle is 3 cm longer than it is wide and its area is 40 cm². Find its dimensions.

Keys: MODE531=3=(−)40==

Calculator: w = 5 and w = −8. A width cannot be negative, so the rectangle is 5 cm × 8 cm.

Example 5: Two equations, two unknowns (MODE 5 1)

Solve x + 2y = 3 and 2x + 3y = 4.

Keys: MODE51, then row 1: 1=2=3=, row 2: 2=3=4=, then =.

Calculator: X = −1, then ▼ shows Y = 2.

Example 6: Three unknowns (MODE 5 2)

Solve x − y + z = 2, x + y − z = 0, −x + y + z = 4.

Keys: MODE52, then enter each row as a, b, c, d: 1=(−)1=1=2=, 1=1=(−)1=0=, (−)1=1=1=4=, then =.

Calculator: X = 1, Y = 2, Z = 3.

Example 7: A cubic (MODE 5 4)

Solve x³ − 2x² − x + 2 = 0. Here a = 1, b = −2, c = −1, d = 2.

Keys: MODE541=(−)2=(−)1=2==, then = for each further root.

Calculator: three roots, x = −1, x = 2 and x = 1.

Bonus: Use TABLE mode (MODE 7) to see the roots

TABLE mode lists f(x) for a range of x, which is a quick way to see where a function crosses zero. For f(x) = x² − 4x + 3: press MODE7, type the function using ALPHA) for X, press =, then answer Start? 0, End? 5, Step? 1. If the calculator asks for g(X) as well (models such as the fx-115ES PLUS can be set up for two functions), press = without typing anything to skip it and get a table of f(x) only.

f(x) = 0 at x = 1 and x = 3, which matches (x − 1)(x − 3) = 0. The smallest value, −1 at x = 2, is the vertex. If a sign change happens between two table values, the root is between them.

5) Why MODE 5 3 gives a “wrong” answer (and how to check it)

The solver itself is reliable. Wrong answers almost always come from the input:

• The equation was not set to 0. 3x² = 5x − 2 must become 3x² − 5x + 2 = 0 first (Example 3).
• A sign was dropped. Use (−) for negative coefficients. Re-read the editor before you press the final =.
• A missing term was skipped. For x² − 9 = 0, b = 0, so enter 1, 0, −9. Skipping b shifts every coefficient.
• The equation was not expanded. (x + 2)(x − 5) = 8 must become x² − 3x − 18 = 0 before you read off a, b and c.
• Wrong mode. If the screen shows “CMPLX”, “STAT” or a matrix, press MODE53 again.

Three checks take seconds:

• Substitute. Put each root into the original equation. Both sides must be equal.
• Sum and product. For ax² + bx + c = 0, the roots add to −b/a and multiply to c/a. In Example 1, −b/a = −1/2 and 1 + (−3/2) = −1/2 ✓; c/a = −3/2 and 1 × (−3/2) = −3/2 ✓.
• Discriminant. b² − 4ac > 0 means two real roots, = 0 one repeated root, < 0 complex roots. If the calculator disagrees, the coefficients are wrong.

The discriminant calculator and quadratic formula calculator walk through the same steps, and the quadratic formula guide explains why they work.

6) Calculator answer vs. showing your work

EQN mode gives roots, not working. In most exams you still have to show how you got them: factoring, completing the square, or the quadratic formula. A good routine is to solve by hand first and use MODE 5 3 as the check, not the other way round. If the two disagree, find the line where your working goes wrong. Many exams also restrict which calculator models you may bring, so check the rules before you rely on EQN mode.

When you need the steps, not just the roots, the guide to getting (and checking) step-by-step solutions shows how to ask a solver for each step, and the quadratic equations step-by-step guide covers factoring and completing the square.

7) A “MODE 5 3 calculator online” with full steps

No Casio with EQN mode? Lost your calculator? You do not need an emulator. MathAI GPT solves the same equations, quadratics, cubics and systems, from a typed line or a photo, and shows every step so you can learn the method as well as get the roots.

• On the web: open the free MathAI GPT solver and type 2x^2 + x - 3 = 0. Nothing to install, and there is a free daily allowance.
• On iPhone: get MathAI GPT - Math Solver on the App Store. Photograph a worksheet problem and get the full solution, then compare it with what your Casio shows.
• On Android: get MathAI GPT on Google Play.

Useful prompts: “Solve 3x^2 = 5x − 2 step by step and check both roots”, or “My Casio says x = 5 and x = −8 for w(w + 3) = 40. Explain which answer fits the problem.”

Frequently asked questions

Try it now

Take one quadratic from your homework, solve it with MODE53, then type it into the MathAI GPT solver and compare its steps with yours. If the roots match and the substitution check works, you are done.