(x-7)^2-25=0

2 min read Jun 17, 2024

Solving the Equation (x-7)^2 - 25 = 0

This article will guide you through solving the equation (x-7)^2 - 25 = 0. This equation is a quadratic equation in disguise, and we can solve it using a few simple steps.

1. Rearranging the Equation

First, we can rearrange the equation to make it easier to work with. Add 25 to both sides:

(x-7)^2 = 25

2. Taking the Square Root

Next, we take the square root of both sides. Remember, when taking the square root, we need to consider both positive and negative solutions:

x - 7 = ±5

3. Solving for x

Now, we can solve for x by adding 7 to both sides:

x = 7 ± 5

4. Finding the Solutions

Finally, we have two possible solutions:

x = 7 + 5 = 12
x = 7 - 5 = 2

Therefore, the solutions to the equation (x-7)^2 - 25 = 0 are x = 12 and x = 2.

Key Points

The equation is a quadratic equation in disguise, as we can expand the square term.
Remember to consider both positive and negative solutions when taking the square root.
You can always check your answers by plugging them back into the original equation.