Questions: Solve the equation by the square root property [ (x-7)^2=64 ] What is the solution set?

Solution Steps

To solve the equation \((x-7)^2 = 64\) using the square root property, we take the square root of both sides of the equation. This will give us two possible solutions because the square root of a number can be both positive and negative. After taking the square root, we solve for \(x\) by isolating it on one side of the equation.

We start with the equation given by the square foot property: \[ (x - 7)^2 = 64 \]

Taking the square root of both sides, we have: \[ x - 7 = \pm 8 \]

Now, we solve for \(x\) by isolating it:

1. For the positive case: \[ x - 7 = 8 \implies x = 15 \]
2. For the negative case: \[ x - 7 = -8 \implies x = -1 \]

Final Answer