2x^2-4x-174=0

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Solution for 2x^2-4x-174=0 equation: 


Simplifying
2x2 + -4x + -174 = 0

Reorder the terms:
-174 + -4x + 2x2 = 0

Solving
-174 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-87 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-87 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-87 + -2x + x2 = 0

Solving
-87 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '87' to each side of the equation.
-87 + -2x + 87 + x2 = 0 + 87

Reorder the terms:
-87 + 87 + -2x + x2 = 0 + 87

Combine like terms: -87 + 87 = 0
0 + -2x + x2 = 0 + 87
-2x + x2 = 0 + 87

Combine like terms: 0 + 87 = 87
-2x + x2 = 87

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 = 87 + 1

Reorder the terms:
1 + -2x + x2 = 87 + 1

Combine like terms: 87 + 1 = 88
1 + -2x + x2 = 88

Factor a perfect square on the left side:
(x + -1)(x + -1) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + -1) equal to 9.38083152 and -9.38083152.


Subproblem 1
x + -1 = 9.38083152

Simplifying
x + -1 = 9.38083152

Reorder the terms:
-1 + x = 9.38083152

Solving
-1 + x = 9.38083152

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 = 9.38083152 + 1

Combine like terms: -1 + 1 = 0
0 + x = 9.38083152 + 1
x = 9.38083152 + 1

Combine like terms: 9.38083152 + 1 = 10.38083152
x = 10.38083152

Simplifying
x = 10.38083152


Subproblem 2
x + -1 = -9.38083152

Simplifying
x + -1 = -9.38083152

Reorder the terms:
-1 + x = -9.38083152

Solving
-1 + x = -9.38083152

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 = -9.38083152 + 1

Combine like terms: -1 + 1 = 0
0 + x = -9.38083152 + 1
x = -9.38083152 + 1

Combine like terms: -9.38083152 + 1 = -8.38083152
x = -8.38083152

Simplifying
x = -8.38083152


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.38083152, -8.38083152}
Solution
x = {10.38083152, -8.38083152}

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