2%E2%88%925%3D0.jpeg "(x−6)2−5=0")
Solving the Quadratic Equation (x−6)²−5=0
This article will guide you through solving the quadratic equation (x−6)²−5=0. We will use the following steps:
1. Simplify the Equation
- Expand the square: (x−6)² = (x−6)(x−6) = x² - 12x + 36
- Substitute: The equation becomes: x² - 12x + 36 - 5 = 0
- Combine like terms: x² - 12x + 31 = 0
2. Solve using the Quadratic Formula
Now that the equation is in standard quadratic form (ax² + bx + c = 0), we can use the quadratic formula to find the solutions for x:
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
- Identify a, b, and c:
- a = 1
- b = -12
- c = 31
- Substitute the values into the formula:
- x = (12 ± √((-12)² - 4 * 1 * 31)) / (2 * 1)
- x = (12 ± √(144 - 124)) / 2
- x = (12 ± √20) / 2
- x = (12 ± 2√5) / 2
- Simplify:
- x = 6 ± √5
3. Solutions
Therefore, the solutions to the equation (x−6)²−5=0 are:
- x = 6 + √5
- x = 6 - √5
These are the two values of x that satisfy the original equation.