Solve the equation by applying the squaring property of equality. Be sure to check all solutions in the original equation.

Question

Quizplus · Accepted Answer

As the equation involves squaring, it is possible to have extraneous solutions. Therefore, it is important to check all solutions in the original equation. If we apply the squaring property of equality, we get:

(x + 7)^2 = 64

Taking the square root, we get:

x + 7 = ±8

Solving for x, we get two solutions:

x = 1 or x = -15

However, we need to check both solutions in the original equation to ensure they are not extraneous.

Checking x = 1:

(1+7)^2 = 64

8^2 = 64

64 = 64

This solution works, so it is valid.

Checking x = -15:

(-15+7)^2 = 64

(-8)^2 = 64

64 = 64

This solution also works, so it is also valid.

Therefore, the correct answer is C as it contains both solutions.

Solve the Equation by Applying the Squaring Property of Equality