Ask a New Question
Menu

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?
Add 3 to both sides of the equation.

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?

1 answer

To solve the quadratic equation \((x - 3)^{25} = 20\), let's go through the steps in order.

First Step:

  • The first step is to take the 25th root of both sides to simplify the equation. This would be mathematically represented as:

\[ x - 3 = \pm 20^{1/25} \]

Solutions:

Now, we can go ahead and solve for \(x\) by adding 3 to both sides of the two possible cases derived from the \(\pm\):

  1. For the positive case: \[ x - 3 = 20^{1/25} \implies x = 3 + 20^{1/25} \]

  2. For the negative case: \[ x - 3 = -20^{1/25} \implies x = 3 - 20^{1/25} \]

Conclusion:

  • One solution is \(x = 3 + 20^{1/25}\).
  • The other solution is \(x = 3 - 20^{1/25}\).

Since specific numerical options were not provided, you would need to determine the approximate decimal values of these expressions to find possible answer choices.