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 of the equation \((x + 9)^2=25\):
\(x + 9=\pm\sqrt{25}\)

Step2: Simplify \(\sqrt{25}\)

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

Step3: Solve for \(x\) in two cases

Case 1: When we take the positive root
\(x+9 = 5\)
Subtract 9 from both sides:
\(x=5 - 9=-4\)
Case 2: When we take the negative root
\(x + 9=-5\)
Subtract 9 from both sides:
\(x=-5 - 9=-14\)

Answer:

The solutions are \(x=-4\) and \(x = - 14\)