2-x(x%2B8)%3D2.jpeg "(x-6)2-x(x+8)=2")
Solving the Quadratic Equation: (x-6)2 - x(x+8) = 2
This article will guide you through the steps of solving the quadratic equation: (x-6)2 - x(x+8) = 2. We will use algebraic manipulation to simplify the equation and ultimately find the solutions for x.
1. Expanding the equation
First, we need to expand the equation by removing the parentheses and simplifying the terms:
(x-6)2 - x(x+8) = 2
- Expand the square: (x-6)2 = (x-6)(x-6) = x² - 12x + 36
- Expand the product: x(x+8) = x² + 8x
- Substitute the expansions: x² - 12x + 36 - (x² + 8x) = 2
2. Simplifying the equation
Now, combine like terms to simplify the equation:
- Combine x² terms: x² - x² = 0
- Combine x terms: -12x - 8x = -20x
- Combine constant terms: 36 - 2 = 34
The simplified equation becomes: -20x + 34 = 0
3. Isolating the variable
To solve for x, we need to isolate the variable on one side of the equation:
- Subtract 34 from both sides: -20x = -34
- Divide both sides by -20: x = -34 / -20
4. Solution
Simplifying the fraction, we get the solution: x = 1.7
Therefore, the solution to the quadratic equation (x-6)2 - x(x+8) = 2 is x = 1.7.