(x-6)^2-5=0

Jasonbradley

2 min read

·

Jun 17, 2024

11

Share

Solving the Quadratic Equation: (x-6)² - 5 = 0

This article will guide you through the steps of solving the quadratic equation (x-6)² - 5 = 0.

Understanding Quadratic Equations

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. These equations can be solved using various methods, including factoring, completing the square, and the quadratic formula.

Solving the Equation

Let's solve the equation (x-6)² - 5 = 0 step by step:

1. Isolate the squared term: Add 5 to both sides of the equation: (x-6)² = 5

2. Take the square root of both sides: √(x-6)² = ±√5 Note that we introduce the ± sign since the square root of a number can be positive or negative.

3. Solve for x: x - 6 = ±√5 x = 6 ± √5

4. The solutions: Therefore, the solutions to the equation (x-6)² - 5 = 0 are:

   • x = 6 + √5
   • x = 6 - √5

Conclusion

By following these steps, we have successfully solved the quadratic equation (x-6)² - 5 = 0. The solutions are x = 6 + √5 and x = 6 - √5. This approach demonstrates how to utilize the properties of square roots and algebraic manipulation to find the roots of a quadratic equation.