Answer the questions about this quadratic equation shown below.

Question

(x−3)25=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 \((x−3)^{25}=20\), we can follow these steps:

First Step:

The first step in solving this equation is to isolate the expression with the variable. Start by taking the 25th root of both sides. Therefore, the first step is:

Take the 25th root of both sides: \[ x - 3 = \pm \sqrt[25]{20} \]

Solutions:

Now we can solve for \(x\) by adding 3 to both sides:

1. For the positive root: \[ x = 3 + \sqrt[25]{20} \]
2. For the negative root: \[ x = 3 - \sqrt[25]{20} \]

Answers:

Based on this, one solution to the quadratic equation is \(x = 3 + \sqrt[25]{20}\) and the other solution is \(x = 3 - \sqrt[25]{20}\).

You would need to select these answers accordingly from the options provided in your material. If there are specific answer choices given, please share them for clarification on which to choose.