8x^2-44x-114=0

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Solution for 8x^2-44x-114=0 equation: 


Simplifying
8x2 + -44x + -114 = 0

Reorder the terms:
-114 + -44x + 8x2 = 0

Solving
-114 + -44x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-57 + -22x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-57 + -22x + 4x2)' equal to zero and attempt to solve:

Simplifying
-57 + -22x + 4x2 = 0

Solving
-57 + -22x + 4x2 = 0

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

Divide each side by '4'.
-14.25 + -5.5x + x2 = 0

Move the constant term to the right:

Add '14.25' to each side of the equation.
-14.25 + -5.5x + 14.25 + x2 = 0 + 14.25

Reorder the terms:
-14.25 + 14.25 + -5.5x + x2 = 0 + 14.25

Combine like terms: -14.25 + 14.25 = 0.00
0.00 + -5.5x + x2 = 0 + 14.25
-5.5x + x2 = 0 + 14.25

Combine like terms: 0 + 14.25 = 14.25
-5.5x + x2 = 14.25

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 14.25 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 14.25 + 7.5625

Combine like terms: 14.25 + 7.5625 = 21.8125
7.5625 + -5.5x + x2 = 21.8125

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 21.8125

Calculate the square root of the right side: 4.670385423

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.670385423 and -4.670385423.


Subproblem 1
x + -2.75 = 4.670385423

Simplifying
x + -2.75 = 4.670385423

Reorder the terms:
-2.75 + x = 4.670385423

Solving
-2.75 + x = 4.670385423

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 4.670385423 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 4.670385423 + 2.75
x = 4.670385423 + 2.75

Combine like terms: 4.670385423 + 2.75 = 7.420385423
x = 7.420385423

Simplifying
x = 7.420385423


Subproblem 2
x + -2.75 = -4.670385423

Simplifying
x + -2.75 = -4.670385423

Reorder the terms:
-2.75 + x = -4.670385423

Solving
-2.75 + x = -4.670385423

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -4.670385423 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -4.670385423 + 2.75
x = -4.670385423 + 2.75

Combine like terms: -4.670385423 + 2.75 = -1.920385423
x = -1.920385423

Simplifying
x = -1.920385423


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.420385423, -1.920385423}
Solution
x = {7.420385423, -1.920385423}

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