Question

solve the equation by the square root property.
$(x + 9)^2 = 25$

Explanation:

Step1: Apply square root property

The square root property states that if \(u^2 = v\), then \(u=\pm\sqrt{v}\). Here, let \(u = x + 9\) and \(v = 25\). So we take the square root of both sides:
\(x + 9=\pm\sqrt{25}\)

Step2: Simplify square root

We know that \(\sqrt{25}=5\), so the equation becomes:
\(x + 9=\pm5\)

Step3: Solve for x (case 1: positive root)

When we take the positive root, we have \(x + 9 = 5\). Subtract 9 from both sides:
\(x=5 - 9=-4\)

Step4: Solve for x (case 2: negative root)

When we take the negative root, we have \(x + 9=-5\). Subtract 9 from both sides:
\(x=-5 - 9=-14\)

Answer:

\(x=-4\) or \(x = - 14\)