Question
Question Answer the questions about this quadratic equation shown below. (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?
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \((x-3)^{25} = 20\), let's break it down step-by-step.
1. **First Step:** The first step in solving the equation is to take the 25th root of both sides. This will allow you to simplify the equation to a more manageable form. Thus, you would express it as:
\[
x - 3 = \pm \sqrt[25]{20}
\]
2. **Finding the Solutions:** From the equation \(x - 3 = \pm \sqrt[25]{20}\), we can isolate \(x\):
\[
x = 3 \pm \sqrt[25]{20}
\]
Therefore, the two solutions can be expressed as:
\(\text{Solution 1: } x_1 = 3 + \sqrt[25]{20}\)
\(\text{Solution 2: } x_2 = 3 - \sqrt[25]{20}\)
If you have specific answer options presented for the solutions, you can choose accordingly based on the expressions derived above.
If you need specific numerical or approximate values for the solutions, you can compute \(\sqrt[25]{20}\) using a calculator. However, the exact solutions can also be reported in the form of \(3 \pm \sqrt[25]{20}\).
1. **First Step:** The first step in solving the equation is to take the 25th root of both sides. This will allow you to simplify the equation to a more manageable form. Thus, you would express it as:
\[
x - 3 = \pm \sqrt[25]{20}
\]
2. **Finding the Solutions:** From the equation \(x - 3 = \pm \sqrt[25]{20}\), we can isolate \(x\):
\[
x = 3 \pm \sqrt[25]{20}
\]
Therefore, the two solutions can be expressed as:
\(\text{Solution 1: } x_1 = 3 + \sqrt[25]{20}\)
\(\text{Solution 2: } x_2 = 3 - \sqrt[25]{20}\)
If you have specific answer options presented for the solutions, you can choose accordingly based on the expressions derived above.
If you need specific numerical or approximate values for the solutions, you can compute \(\sqrt[25]{20}\) using a calculator. However, the exact solutions can also be reported in the form of \(3 \pm \sqrt[25]{20}\).
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