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

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

Transcript text: 1) Rewrite the equation by completing the square. Your equation should look like $(x+c)^{2}=d$ or $(x-c)^{2}=d$. \[ (x-7)^{2}=100 \rightarrow \frac{7 x}{+x} \] 2) What are the solutions to the equation? Choose 1 answer: (A) $x=7 \pm \sqrt{10}$ (B) $x=-7 \pm \sqrt{10}$ (C) $x=7 \pm 10$ (D) $x=-7 \pm 10$

Solution

Solution Steps

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

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.
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 $x$.

Step 1: Identify the Equation

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

Step 2: Solve the Equation

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

Step 3: Calculate the Solutions

Calculate the two possible values for $x$: