8x^2-4x-94=0

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Solution for 8x^2-4x-94=0 equation: 


Simplifying
8x2 + -4x + -94 = 0

Reorder the terms:
-94 + -4x + 8x2 = 0

Solving
-94 + -4x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + -2x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-47 + -2x + 4x2)' equal to zero and attempt to solve:

Simplifying
-47 + -2x + 4x2 = 0

Solving
-47 + -2x + 4x2 = 0

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

Divide each side by '4'.
-11.75 + -0.5x + x2 = 0

Move the constant term to the right:

Add '11.75' to each side of the equation.
-11.75 + -0.5x + 11.75 + x2 = 0 + 11.75

Reorder the terms:
-11.75 + 11.75 + -0.5x + x2 = 0 + 11.75

Combine like terms: -11.75 + 11.75 = 0.00
0.00 + -0.5x + x2 = 0 + 11.75
-0.5x + x2 = 0 + 11.75

Combine like terms: 0 + 11.75 = 11.75
-0.5x + x2 = 11.75

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 11.75 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 11.75 + 0.0625

Combine like terms: 11.75 + 0.0625 = 11.8125
0.0625 + -0.5x + x2 = 11.8125

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 11.8125

Calculate the square root of the right side: 3.436931771

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.436931771 and -3.436931771.


Subproblem 1
x + -0.25 = 3.436931771

Simplifying
x + -0.25 = 3.436931771

Reorder the terms:
-0.25 + x = 3.436931771

Solving
-0.25 + x = 3.436931771

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 3.436931771 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 3.436931771 + 0.25
x = 3.436931771 + 0.25

Combine like terms: 3.436931771 + 0.25 = 3.686931771
x = 3.686931771

Simplifying
x = 3.686931771


Subproblem 2
x + -0.25 = -3.436931771

Simplifying
x + -0.25 = -3.436931771

Reorder the terms:
-0.25 + x = -3.436931771

Solving
-0.25 + x = -3.436931771

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -3.436931771 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -3.436931771 + 0.25
x = -3.436931771 + 0.25

Combine like terms: -3.436931771 + 0.25 = -3.186931771
x = -3.186931771

Simplifying
x = -3.186931771


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.686931771, -3.186931771}
Solution
x = {3.686931771, -3.186931771}

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