8x^2+12x-13=0

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Solution for 8x^2+12x-13=0 equation:


Simplifying
8x2 + 12x + -13 = 0

Reorder the terms:
-13 + 12x + 8x2 = 0

Solving
-13 + 12x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.625 + 1.5x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + 1.5x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + 1.5x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + 1.5x + x2 = 0 + 1.625
1.5x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
1.5x + x2 = 1.625

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 = 1.625 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 1.625 + 0.5625

Combine like terms: 1.625 + 0.5625 = 2.1875
0.5625 + 1.5x + x2 = 2.1875

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 2.1875

Calculate the square root of the right side: 1.479019946

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.479019946 and -1.479019946.

Subproblem 1

x + 0.75 = 1.479019946 Simplifying x + 0.75 = 1.479019946 Reorder the terms: 0.75 + x = 1.479019946 Solving 0.75 + x = 1.479019946 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 = 1.479019946 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.479019946 + -0.75 x = 1.479019946 + -0.75 Combine like terms: 1.479019946 + -0.75 = 0.729019946 x = 0.729019946 Simplifying x = 0.729019946

Subproblem 2

x + 0.75 = -1.479019946 Simplifying x + 0.75 = -1.479019946 Reorder the terms: 0.75 + x = -1.479019946 Solving 0.75 + x = -1.479019946 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 = -1.479019946 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.479019946 + -0.75 x = -1.479019946 + -0.75 Combine like terms: -1.479019946 + -0.75 = -2.229019946 x = -2.229019946 Simplifying x = -2.229019946

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.729019946, -2.229019946}

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