8x^2-40x-679=0

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Solution for 8x^2-40x-679=0 equation:


Simplifying
8x2 + -40x + -679 = 0

Reorder the terms:
-679 + -40x + 8x2 = 0

Solving
-679 + -40x + 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'.
-84.875 + -5x + x2 = 0

Move the constant term to the right:

Add '84.875' to each side of the equation.
-84.875 + -5x + 84.875 + x2 = 0 + 84.875

Reorder the terms:
-84.875 + 84.875 + -5x + x2 = 0 + 84.875

Combine like terms: -84.875 + 84.875 = 0.000
0.000 + -5x + x2 = 0 + 84.875
-5x + x2 = 0 + 84.875

Combine like terms: 0 + 84.875 = 84.875
-5x + x2 = 84.875

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 84.875 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 84.875 + 6.25

Combine like terms: 84.875 + 6.25 = 91.125
6.25 + -5x + x2 = 91.125

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 91.125

Calculate the square root of the right side: 9.545941546

Break this problem into two subproblems by setting 
(x + -2.5) equal to 9.545941546 and -9.545941546.

Subproblem 1

x + -2.5 = 9.545941546 Simplifying x + -2.5 = 9.545941546 Reorder the terms: -2.5 + x = 9.545941546 Solving -2.5 + x = 9.545941546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.545941546 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.545941546 + 2.5 x = 9.545941546 + 2.5 Combine like terms: 9.545941546 + 2.5 = 12.045941546 x = 12.045941546 Simplifying x = 12.045941546

Subproblem 2

x + -2.5 = -9.545941546 Simplifying x + -2.5 = -9.545941546 Reorder the terms: -2.5 + x = -9.545941546 Solving -2.5 + x = -9.545941546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.545941546 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.545941546 + 2.5 x = -9.545941546 + 2.5 Combine like terms: -9.545941546 + 2.5 = -7.045941546 x = -7.045941546 Simplifying x = -7.045941546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.045941546, -7.045941546}

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