(x-7)^2=60

2 min read Jun 17, 2024

Solving the Equation (x-7)² = 60

This article will guide you through the steps to solve the equation (x-7)² = 60. This is a quadratic equation in disguise, and we'll use the square root property and basic algebraic manipulation to find the solutions.

Step 1: Take the Square Root of Both Sides

The first step is to isolate the squared term. Since we have a squared term on the left side, we can take the square root of both sides. Remember that when taking the square root of a number, we must consider both positive and negative solutions.

√(x-7)² = ±√60

This simplifies to:

x-7 = ±√60

Step 2: Simplify the Radical

We can simplify the radical on the right side. The prime factorization of 60 is 2 x 2 x 3 x 5, so we can take out a pair of 2s:

x-7 = ±2√15

Step 3: Isolate x

To isolate x, we need to add 7 to both sides of the equation:

x = 7 ± 2√15

Step 4: Solutions

This gives us our two solutions:

x = 7 + 2√15
x = 7 - 2√15

Therefore, the solutions to the equation (x-7)² = 60 are x = 7 + 2√15 and x = 7 - 2√15.