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.