(x+1/2)^2-(x+1/2)(x+6)=8

2 min read Jun 16, 2024
(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.

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