Question

nswer the questions about this quadratic equation shown below.

(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 \((x - 3)^2/5 = 20\), let's go through the questions step by step.

1. **What should be the first step when solving the quadratic equation above?**

The first step is to eliminate the fraction by multiplying both sides of the equation by 5. This gives:
\[
(x - 3)^2 = 100
\]

2. **Which of the following is one of the solutions to the quadratic equation above?**

To find the solutions, take the square root of both sides after simplifying the equation:
\[
x - 3 = \pm 10
\]
This leads to two equations:
- \(x - 3 = 10\)
- \(x - 3 = -10\)

Solving these gives:
- For \(x - 3 = 10\): \(x = 13\)
- For \(x - 3 = -10\): \(x = -7\)

Therefore, one of the solutions is **13** and the other is **-7**.

3. **Which of the following is the other solution to the quadratic equation above?**

As we solved above, if one solution is \(13\), then the other solution is \(-7\).

In summary:
- **First step:** Multiply both sides by 5 to eliminate the fraction.
- **One solution:** 13.
- **Other solution:** -7.