(x−6)2−5=0 Least To Greatest

2 min read Jun 17, 2024

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 and finding the solutions in order from least to greatest.

Understanding the Equation

The equation (x-6)² - 5 = 0 is a quadratic equation in standard form, which is ax² + bx + c = 0. In this case:

a = 1 (the coefficient of x²)
b = -12 (the coefficient of x)
c = 31 (the constant term)

Solving for x

We can solve for x using the following steps:

Isolate the squared term:
- Add 5 to both sides of the equation: (x-6)² = 5
Take the square root of both sides:
- √(x-6)² = ±√5
Simplify:
- x - 6 = ±√5
Isolate x:
- x = 6 ±√5

Finding the Solutions

This gives us two solutions:

x = 6 + √5 (approximately 8.24)
x = 6 - √5 (approximately 3.76)

Ordering the Solutions

Since 3.76 is less than 8.24, the solutions in order from least to greatest are:

x = 6 - √5, x = 6 + √5

Therefore, the solutions to the equation (x-6)² - 5 = 0, ordered from least to greatest, are 3.76 and 8.24.