It is the method used to solve for the solutions/roots of a quadratic equation [tex]x^2 = k[/tex].

A. extracting square roots

B. completing the square

C. factoring

D. quadratic formula

The method used to solve for the solutions/roots of the quadratic equation x 2 = k is called extracting square roots. This technique allows for finding the roots directly by taking the square root of both sides of the equation. In summary, the answer is A. extracting square roots.
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Answered by Anonymous | 2025-07-04

To find the solutions or roots of a quadratic equation given in the form x 2 = k , the method used is 'extracting square roots'. This is a straightforward method when dealing with equations where the variable is perfectly squared and set equal to a constant.
Here's how to solve it:

Start with the equation: x 2 = k

Take the square root of both sides: To isolate x , take the square root of both sides of the equation. Remember, taking the square root introduces a positive and a negative solution. x = ± k ​

Write the solutions: The solutions (roots) of the equation x 2 = k are x = k ​ and x = − k ​ .


Example:
Suppose we have the equation x 2 = 9 .

Taking the square root of both sides gives: x = ± 9 ​

Simplifying gives the roots: x = 3 and x = − 3


This method is most efficient when the quadratic equation is already isolated like this or can be easily rearranged to this form. In other cases, such as when the equation is more complex (for example, a x 2 + b x + c = 0 with non-zero b or c ), other methods like the quadratic formula, factoring, or completing the square might be more appropriate.

Answered by LiamAlexanderSmith | 2025-07-06