2x^2+176x-408=0

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Solution for 2x^2+176x-408=0 equation: 


Simplifying
2x2 + 176x + -408 = 0

Reorder the terms:
-408 + 176x + 2x2 = 0

Solving
-408 + 176x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-204 + 88x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-204 + 88x + x2)' equal to zero and attempt to solve:

Simplifying
-204 + 88x + x2 = 0

Solving
-204 + 88x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '204' to each side of the equation.
-204 + 88x + 204 + x2 = 0 + 204

Reorder the terms:
-204 + 204 + 88x + x2 = 0 + 204

Combine like terms: -204 + 204 = 0
0 + 88x + x2 = 0 + 204
88x + x2 = 0 + 204

Combine like terms: 0 + 204 = 204
88x + x2 = 204

The x term is 88x.  Take half its coefficient (44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
88x + 1936 + x2 = 204 + 1936

Reorder the terms:
1936 + 88x + x2 = 204 + 1936

Combine like terms: 204 + 1936 = 2140
1936 + 88x + x2 = 2140

Factor a perfect square on the left side:
(x + 44)(x + 44) = 2140

Calculate the square root of the right side: 46.260134025

Break this problem into two subproblems by setting 
(x + 44) equal to 46.260134025 and -46.260134025.


Subproblem 1
x + 44 = 46.260134025

Simplifying
x + 44 = 46.260134025

Reorder the terms:
44 + x = 46.260134025

Solving
44 + x = 46.260134025

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = 46.260134025 + -44

Combine like terms: 44 + -44 = 0
0 + x = 46.260134025 + -44
x = 46.260134025 + -44

Combine like terms: 46.260134025 + -44 = 2.260134025
x = 2.260134025

Simplifying
x = 2.260134025


Subproblem 2
x + 44 = -46.260134025

Simplifying
x + 44 = -46.260134025

Reorder the terms:
44 + x = -46.260134025

Solving
44 + x = -46.260134025

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = -46.260134025 + -44

Combine like terms: 44 + -44 = 0
0 + x = -46.260134025 + -44
x = -46.260134025 + -44

Combine like terms: -46.260134025 + -44 = -90.260134025
x = -90.260134025

Simplifying
x = -90.260134025


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.260134025, -90.260134025}
Solution
x = {2.260134025, -90.260134025}

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