2(x^2+x-87)=0

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Solution for 2(x^2+x-87)=0 equation: 


Simplifying
2(x2 + x + -87) = 0

Reorder the terms:
2(-87 + x + x2) = 0
(-87 * 2 + x * 2 + x2 * 2) = 0
(-174 + 2x + 2x2) = 0

Solving
-174 + 2x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
-87 + x + x2 = 0

Solving
-87 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 87 + 0.25

Reorder the terms:
0.25 + x + x2 = 87 + 0.25

Combine like terms: 87 + 0.25 = 87.25
0.25 + x + x2 = 87.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 87.25

Calculate the square root of the right side: 9.340770846

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.340770846 and -9.340770846.


Subproblem 1
x + 0.5 = 9.340770846

Simplifying
x + 0.5 = 9.340770846

Reorder the terms:
0.5 + x = 9.340770846

Solving
0.5 + x = 9.340770846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 9.340770846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.340770846 + -0.5
x = 9.340770846 + -0.5

Combine like terms: 9.340770846 + -0.5 = 8.840770846
x = 8.840770846

Simplifying
x = 8.840770846


Subproblem 2
x + 0.5 = -9.340770846

Simplifying
x + 0.5 = -9.340770846

Reorder the terms:
0.5 + x = -9.340770846

Solving
0.5 + x = -9.340770846

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -9.340770846 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.340770846 + -0.5
x = -9.340770846 + -0.5

Combine like terms: -9.340770846 + -0.5 = -9.840770846
x = -9.840770846

Simplifying
x = -9.840770846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.840770846, -9.840770846}
Solution
x = {8.840770846, -9.840770846}

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