4x^2-8x-172=0

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Solution for 4x^2-8x-172=0 equation: 


Simplifying
4x2 + -8x + -172 = 0

Reorder the terms:
-172 + -8x + 4x2 = 0

Solving
-172 + -8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-43 + -2x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-43 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-43 + -2x + x2 = 0

Solving
-43 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -2x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + -2x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2x + x2 = 0 + 43
-2x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
-2x + x2 = 43

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 43 + 1

Reorder the terms:
1 + -2x + x2 = 43 + 1

Combine like terms: 43 + 1 = 44
1 + -2x + x2 = 44

Factor a perfect square on the left side:
(x + -1)(x + -1) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -1) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + -1 = 6.633249581

Simplifying
x + -1 = 6.633249581

Reorder the terms:
-1 + x = 6.633249581

Solving
-1 + x = 6.633249581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.633249581 + 1
x = 6.633249581 + 1

Combine like terms: 6.633249581 + 1 = 7.633249581
x = 7.633249581

Simplifying
x = 7.633249581


Subproblem 2
x + -1 = -6.633249581

Simplifying
x + -1 = -6.633249581

Reorder the terms:
-1 + x = -6.633249581

Solving
-1 + x = -6.633249581

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.633249581 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.633249581 + 1
x = -6.633249581 + 1

Combine like terms: -6.633249581 + 1 = -5.633249581
x = -5.633249581

Simplifying
x = -5.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.633249581, -5.633249581}
Solution
x = {7.633249581, -5.633249581}

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