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

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.

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

$$x - 21 = \pm \sqrt{25}$$

This simplifies to:

$$x - 21 = \pm 5$$

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