8x^2-12x-14=-9

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Solution for 8x^2-12x-14=-9 equation:


Simplifying
8x2 + -12x + -14 = -9

Reorder the terms:
-14 + -12x + 8x2 = -9

Solving
-14 + -12x + 8x2 = -9

Solving for variable 'x'.

Reorder the terms:
-14 + 9 + -12x + 8x2 = -9 + 9

Combine like terms: -14 + 9 = -5
-5 + -12x + 8x2 = -9 + 9

Combine like terms: -9 + 9 = 0
-5 + -12x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.625 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -1.5x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -1.5x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -1.5x + x2 = 0 + 0.625
-1.5x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-1.5x + x2 = 0.625

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 0.625 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.625 + 0.5625

Combine like terms: 0.625 + 0.5625 = 1.1875
0.5625 + -1.5x + x2 = 1.1875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.1875

Calculate the square root of the right side: 1.089724736

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.089724736 and -1.089724736.

Subproblem 1

x + -0.75 = 1.089724736 Simplifying x + -0.75 = 1.089724736 Reorder the terms: -0.75 + x = 1.089724736 Solving -0.75 + x = 1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.089724736 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.089724736 + 0.75 x = 1.089724736 + 0.75 Combine like terms: 1.089724736 + 0.75 = 1.839724736 x = 1.839724736 Simplifying x = 1.839724736

Subproblem 2

x + -0.75 = -1.089724736 Simplifying x + -0.75 = -1.089724736 Reorder the terms: -0.75 + x = -1.089724736 Solving -0.75 + x = -1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.089724736 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.089724736 + 0.75 x = -1.089724736 + 0.75 Combine like terms: -1.089724736 + 0.75 = -0.339724736 x = -0.339724736 Simplifying x = -0.339724736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.839724736, -0.339724736}

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