When you can isolate a squared term, this is one of the cleanest methods. The key is the ± rule.
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Solve Now →Solving by square roots works when the quadratic can be written in a form where a squared expression is isolated, such as:
This often happens when the middle term is missing (b = 0), or when the quadratic is already a perfect square (or can become one after a small rewrite).
If you want a few more examples specifically for the “solve by square roots” approach, Purplemath’s guide to solving quadratics is a helpful reference.
The biggest reason students miss solutions is forgetting the plus/minus. If you have:
then x can be 3 or -3, because 3² = 9 and (-3)² = 9. That's why we write:
💡 Quick memory trick
Square roots while solving equations always come with ± (unless you are taking a principal square root in other contexts).
Use addition/subtraction to move constants, and division to make the coefficient 1 if needed. Your goal is x² = k or (x − h)² = k.
When you take the square root, include ±: x = ±√k or x − h = ±√k.
If you have x − h = ±√k, add h to both sides.
Always plug both answers back into the original equation.
Example 1: No middle term
Solve: 2x² - 18 = 0
Example 2: Isolate x² first
Solve: x² + 7 = 23
Example 3: Perfect square form
Solve: (x - 3)² = 16
Example 4: No real solutions (negative k)
Solve: x² = -9
Checking is especially important when you manipulate square roots. It also catches algebra mistakes. If your equation is already in a squared form, it's usually safe—but checking takes seconds and can save you from losing points.
For a full overview of solving quadratics (including factoring, completing the square, and the quadratic formula), start here: how to solve a quadratic equation step by step.
Forgetting ±
This is the #1 mistake. Always write x = ±√k.
Taking √(a + b) as √a + √b
That rule is NOT true in general (e.g., √(9+16) ≠ √9 + √16).
Not isolating the square first
Make sure the square is alone before taking the square root.
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