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 quadratic equation \((x−3)^2/5=20\), follow these steps:

First Step:

1. Eliminate the fraction: Multiply both sides of the equation by 5 to eliminate the denominator. \[ (x - 3)^2 = 100 \]

Solutions:

2. Take the square root of both sides: From \((x - 3)^2 = 100\), take the square root of both sides. Remember to consider both the positive and negative square roots. \[ x - 3 = 10 \quad \text{or} \quad x - 3 = -10 \]

3. Solve for \(x\):

   • From \(x - 3 = 10\): \[ x = 10 + 3 = 13 \]
   • From \(x - 3 = -10\): \[ x = -10 + 3 = -7 \]

Answers:

• One solution to the quadratic equation is \(x = 13\).
• The other solution to the quadratic equation is \(x = -7\).

Thus, the answers to your questions are:

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