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 \(\frac{(x−3)^2}{5} = 20\), let's go through the steps outlined in your questions.

First step:

1. Isolate the quadratic expression: To eliminate the fraction, multiply both sides by 5. \[ (x−3)^2 = 100 \]

Finding solutions:

2. Taking the square root: Now, take the square root of both sides. Remember to consider both the positive and negative roots. \[ x−3 = \pm 10 \] This gives us two equations: \[ x - 3 = 10 \quad \text{and} \quad x - 3 = -10 \]

3. Solving for \(x\):

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

Solutions:

Thus, the two solutions to the quadratic equation \(\frac{(x−3)^2}{5} = 20\) are:

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

Answers:

• First step: Multiply both sides by \(5\) to eliminate the fraction.
• One solution: \(x = 13\)
• Other solution: \(x = -7\)