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:

1. First Step: The first step is to isolate the expression on one side. This can be done by taking the 25th root of both sides. Thus, we can rewrite the equation as: \[ x - 3 = \pm \sqrt[25]{20} \]

2. Finding Solutions: We can now solve for \(x\): \[ x = 3 \pm \sqrt[25]{20} \]

Now, let’s denote the two solutions explicitly:

• The first solution (using the positive root) would be: \[ x_1 = 3 + \sqrt[25]{20} \]

• The second solution (using the negative root) would be: \[ x_2 = 3 - \sqrt[25]{20} \]

So to summarize, here are the answers to your questions:

1. The first step when solving the quadratic equation is to take the 25th root of both sides of the equation.
2. One of the solutions is \(x_1 = 3 + \sqrt[25]{20}\).
3. The other solution is \(x_2 = 3 - \sqrt[25]{20}\).