(x+7)^2-7=25

2 min read Jun 17, 2024

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

This article will guide you through the steps to solve the equation (x + 7)² - 7 = 25. We will use algebraic manipulation to isolate the variable 'x' and find its value.

Step 1: Isolate the Squared Term

Add 7 to both sides of the equation: This removes the constant term from the left side. (x + 7)² - 7 + 7 = 25 + 7 (x + 7)² = 32

Step 2: Take the Square Root of Both Sides

Take the square root of both sides of the equation: This eliminates the square from the left side. Remember that taking the square root can result in both positive and negative solutions. √(x + 7)² = ±√32
Simplify the square root on the right side: x + 7 = ±√(16 * 2) = ±4√2

Step 3: Isolate 'x'

Subtract 7 from both sides of the equation: This isolates the variable 'x'. x + 7 - 7 = ±4√2 - 7
Simplify: x = -7 ± 4√2

Solutions

Therefore, the solutions to the equation (x + 7)² - 7 = 25 are:

x = -7 + 4√2
x = -7 - 4√2

These are the two possible values of 'x' that satisfy the original equation.