(x-7)^2=64/49

Jasonbradley

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Jun 17, 2024

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Solving for x in the Equation (x-7)² = 64/49

This article will guide you through the steps to solve the equation (x-7)² = 64/49.

Understanding the Equation

The equation represents a quadratic equation with a perfect square on the left side. To solve for x, we'll utilize the concept of square roots.

Solving the Equation

1. Take the square root of both sides:

   • √[(x-7)²] = ±√(64/49)

2. Simplify:

   • (x-7) = ±(8/7)

3. Isolate x:

   • x = 7 ± (8/7)

4. Solve for both possible solutions:

   • Solution 1: x = 7 + (8/7) = 57/7
   • Solution 2: x = 7 - (8/7) = 41/7

Therefore, the solutions to the equation (x-7)² = 64/49 are x = 57/7 and x = 41/7.

Note: It's important to remember that when taking the square root of both sides of an equation, we need to consider both positive and negative roots. This is why we have two solutions for x.