%5E2-(x%2B1%2F2)(x%2B6)%3D8.jpeg "(x+1/2)^2-(x+1/2)(x+6)=8")
Solving the Equation: (x + 1/2)^2 - (x + 1/2)(x + 6) = 8
This article will guide you through the steps to solve the given quadratic equation. We will use algebraic manipulation and the quadratic formula to find the solutions.
Step 1: Expanding the Equation
First, we need to expand the equation by multiplying out the brackets:
- (x + 1/2)^2: This expands to x² + x + 1/4
- (x + 1/2)(x + 6): This expands to x² + 6.5x + 3
Substituting these back into the original equation, we get:
x² + x + 1/4 - (x² + 6.5x + 3) = 8
Step 2: Simplifying the Equation
Now, we simplify the equation by combining like terms:
x² + x + 1/4 - x² - 6.5x - 3 = 8
-5.5x - 11/4 = 8
Step 3: Isolating the x Term
To isolate the x term, we move the constant term to the right side of the equation:
-5.5x = 8 + 11/4
-5.5x = 43/4
Step 4: Solving for x
Finally, we solve for x by dividing both sides of the equation by -5.5:
x = (43/4) / (-5.5)
x = -1.95 (approximately)
Conclusion
Therefore, the solution to the equation (x + 1/2)^2 - (x + 1/2)(x + 6) = 8 is x = -1.95. You can verify this solution by substituting it back into the original equation.