Questions: 1) Rewrite the equation by completing the square. Your equation should look like (x+c)^2=d or (x-c)^2=d. (x-7)^2=100 → 7 x / +x 2) What are the solutions to the equation? Choose 1 answer: (A) x=7 ± √10 (B) x=-7 ± √10 (C) x=7 ± 10 (D) x=-7 ± 10

Solution Steps

To solve the given problems, we need to follow these steps:

1. Completing the Square: The given equation is already in the form \((x-7)^2 = 100\). This is the completed square form, so no further action is needed for this part.

2. Solving the Equation: To find the solutions to the equation \((x-7)^2 = 100\), we take the square root of both sides, which gives us two possible solutions: \(x-7 = 10\) and \(x-7 = -10\). Solving these equations will give us the values of \(x\).

The given equation is already in the form of a completed square: \[ (x-7)^2 = 100 \]

To find the solutions for \(x\), we take the square root of both sides of the equation: \[ x - 7 = \pm \sqrt{100} \]

Calculate the two possible values for \(x\):

1. \(x - 7 = 10\) leads to \(x = 17\)
2. \(x - 7 = -10\) leads to \(x = -3\)

Final Answer