x^2-10x-87=0

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Solution for x^2-10x-87=0 equation: 


Simplifying
x2 + -10x + -87 = 0

Reorder the terms:
-87 + -10x + x2 = 0

Solving
-87 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '87' to each side of the equation.
-87 + -10x + 87 + x2 = 0 + 87

Reorder the terms:
-87 + 87 + -10x + x2 = 0 + 87

Combine like terms: -87 + 87 = 0
0 + -10x + x2 = 0 + 87
-10x + x2 = 0 + 87

Combine like terms: 0 + 87 = 87
-10x + x2 = 87

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 87 + 25

Reorder the terms:
25 + -10x + x2 = 87 + 25

Combine like terms: 87 + 25 = 112
25 + -10x + x2 = 112

Factor a perfect square on the left side:
(x + -5)(x + -5) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -5) equal to 10.583005244 and -10.583005244.


Subproblem 1
x + -5 = 10.583005244

Simplifying
x + -5 = 10.583005244

Reorder the terms:
-5 + x = 10.583005244

Solving
-5 + x = 10.583005244

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 10.583005244 + 5

Combine like terms: -5 + 5 = 0
0 + x = 10.583005244 + 5
x = 10.583005244 + 5

Combine like terms: 10.583005244 + 5 = 15.583005244
x = 15.583005244

Simplifying
x = 15.583005244


Subproblem 2
x + -5 = -10.583005244

Simplifying
x + -5 = -10.583005244

Reorder the terms:
-5 + x = -10.583005244

Solving
-5 + x = -10.583005244

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -10.583005244 + 5

Combine like terms: -5 + 5 = 0
0 + x = -10.583005244 + 5
x = -10.583005244 + 5

Combine like terms: -10.583005244 + 5 = -5.583005244
x = -5.583005244

Simplifying
x = -5.583005244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.583005244, -5.583005244}

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