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?

Answer 1

To solve the quadratic equation \((x - 3)^{25} = 20\), let's break down the questions step by step:

Step 1: First Step to Solve the Equation

The first step when solving the equation \((x - 3)^{25} = 20\) is to take the 25th root of both sides to eliminate the exponent on the left side: \[ x - 3 = \pm \sqrt[25]{20} \] This will give us two cases to solve for \(x\).

Step 2: Solutions to the Quadratic Equation

After taking the 25th root of both sides, we find two scenarios:

1. \(x - 3 = \sqrt[25]{20}\)
2. \(x - 3 = -\sqrt[25]{20}\)

Now we can solve for \(x\) for both scenarios:

1. For \(x - 3 = \sqrt[25]{20}\): \[ x = 3 + \sqrt[25]{20} \]
2. For \(x - 3 = -\sqrt[25]{20}\): \[ x = 3 - \sqrt[25]{20} \]

So, the two solutions to the quadratic equation are:

1. \(x = 3 + \sqrt[25]{20}\)
2. \(x = 3 - \sqrt[25]{20}\)

Summary:

• First Step: Take the 25th root of both sides, resulting in \(x - 3 = \pm \sqrt[25]{20}\).
• One Solution: \(x = 3 + \sqrt[25]{20}\)
• Other Solution: \(x = 3 - \sqrt[25]{20}\)

If you have specific answer choices for the solutions, please provide them so I can help identify which ones correspond to the solutions derived!