Question

Answer the questions about this quadratic equation shown below ((x - 3) ^ 2)/5 = 20 ( points) What should be the first step when solving the quadratic equation above? Which of the following is one of the solutions to the quadratic equation above ? Which of the following is the other solution to the quadratic equation above?

Answer 1

To solve the quadratic equation \(\frac{(x - 3)^2}{5} = 20\), we can follow these steps:

### First Step
The first step when solving the equation is to eliminate the fraction. We can do this by multiplying both sides of the equation by 5:

\[
(x - 3)^2 = 100
\]

### Finding Solutions
Next, we can take the square root of both sides:

\[
x - 3 = \pm10
\]

This gives us two separate equations to solve:

1. \(x - 3 = 10\)
2. \(x - 3 = -10\)

Solving these equations:

1. From \(x - 3 = 10\):
\[
x = 10 + 3 = 13
\]

2. From \(x - 3 = -10\):
\[
x = -10 + 3 = -7
\]

### Solutions
Therefore, the two solutions to the quadratic equation are:
- One solution is \(x = 13\).
- The other solution is \(x = -7\).

If you have options provided to select from for the solutions, you can identify \(13\) and \(-7\) as the correct choices based on the above calculations.