(x-5)^2=7

2 min read Jun 17, 2024

Solving the Equation: (x - 5)^2 = 7

This equation represents a quadratic equation in a slightly disguised form. Let's break down how to solve for the values of 'x' that satisfy this equation.

Understanding the Equation

The equation (x - 5)^2 = 7 essentially asks: "What number, when decreased by 5 and then squared, results in 7?" To find this number, we'll need to isolate 'x'.

Solving for 'x'

Square Root Both Sides: Start by taking the square root of both sides of the equation. Remember that taking the square root can result in both positive and negative solutions.

√((x - 5)^2) = ±√7
Simplify: The square root of (x - 5)^2 is simply (x - 5).

x - 5 = ±√7
Isolate 'x': Add 5 to both sides of the equation.

x = 5 ±√7

Solutions

Therefore, the solutions to the equation (x - 5)^2 = 7 are:

x = 5 + √7
x = 5 - √7

These are the two values of 'x' that, when substituted back into the original equation, will make the equation true.

Important Note:

Remember to consider both the positive and negative square roots when solving equations involving squares.