Answer the questions about this quadratic equation shown below.

Question

(x−3)^2/5=20


(3 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 equation \((x−3)^2/5 = 20\), let's break it down step by step.

1. First Step: The first step in solving the given quadratic equation is to eliminate the fraction by multiplying both sides by 5. This will give you:

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

2. Finding the Solutions: To find the solutions, we take the square root of both sides:

\[ x - 3 = \pm 10 \]

This leads to two cases:

• Case 1: \(x - 3 = 10 \Rightarrow x = 10 + 3 = 13\)
• Case 2: \(x - 3 = -10 \Rightarrow x = -10 + 3 = -7\)

Thus, the solutions are:

• One solution is \(x = 13\)
• The other solution is \(x = -7\)

Summary of Answers:

1. The first step is to multiply both sides by 5.
2. One of the solutions is \(x = 13\).
3. The other solution is \(x = -7\).