8x^2-6x-7=0

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Solution for 8x^2-6x-7=0 equation: 


Simplifying
8x2 + -6x + -7 = 0

Reorder the terms:
-7 + -6x + 8x2 = 0

Solving
-7 + -6x + 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'.
-0.875 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.75x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.75x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.75x + x2 = 0 + 0.875
-0.75x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.75x + x2 = 0.875

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.875 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.875 + 0.140625

Combine like terms: 0.875 + 0.140625 = 1.015625
0.140625 + -0.75x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.007782219 and -1.007782219.


Subproblem 1
x + -0.375 = 1.007782219

Simplifying
x + -0.375 = 1.007782219

Reorder the terms:
-0.375 + x = 1.007782219

Solving
-0.375 + x = 1.007782219

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.007782219 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.007782219 + 0.375
x = 1.007782219 + 0.375

Combine like terms: 1.007782219 + 0.375 = 1.382782219
x = 1.382782219

Simplifying
x = 1.382782219


Subproblem 2
x + -0.375 = -1.007782219

Simplifying
x + -0.375 = -1.007782219

Reorder the terms:
-0.375 + x = -1.007782219

Solving
-0.375 + x = -1.007782219

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.007782219 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.007782219 + 0.375
x = -1.007782219 + 0.375

Combine like terms: -1.007782219 + 0.375 = -0.632782219
x = -0.632782219

Simplifying
x = -0.632782219


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.382782219, -0.632782219}

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