Questions: What are the solutions to the equation (x-21)^2=25?

What are the solutions to the equation (x-21)^2=25?
Transcript text: What are the solutions to the equation $(x-21)^{2}=25 ?$
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Solution

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Solution Steps

To solve the equation \((x-21)^2 = 25\), we need to take the square root of both sides of the equation. This will give us two possible solutions because the square root of a number can be both positive and negative. After taking the square root, we solve for \(x\) by isolating it on one side of the equation.

Step 1: Take the Square Root

Starting with the equation \((x - 21)^2 = 25\), we take the square root of both sides:

\[ x - 21 = \pm \sqrt{25} \]

This simplifies to:

\[ x - 21 = \pm 5 \]

Step 2: Solve for \(x\)

We now have two equations to solve:

  1. \(x - 21 = 5\)
  2. \(x - 21 = -5\)

For the first equation:

\[ x = 21 + 5 = 26 \]

For the second equation:

\[ x = 21 - 5 = 16 \]

Final Answer

The solutions to the equation are:

\[ \boxed{x = 26} \quad \text{and} \quad \boxed{x = 16} \]

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