x^2-10x-25=36

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Solution for x^2-10x-25=36 equation: 


Simplifying
x2 + -10x + -25 = 36

Reorder the terms:
-25 + -10x + x2 = 36

Solving
-25 + -10x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
-25 + -36 + -10x + x2 = 36 + -36

Combine like terms: -25 + -36 = -61
-61 + -10x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-61 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + -10x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + -10x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + -10x + x2 = 0 + 61
-10x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
-10x + x2 = 61

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 = 61 + 25

Reorder the terms:
25 + -10x + x2 = 61 + 25

Combine like terms: 61 + 25 = 86
25 + -10x + x2 = 86

Factor a perfect square on the left side:
(x + -5)(x + -5) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -5) equal to 9.273618495 and -9.273618495.


Subproblem 1
x + -5 = 9.273618495

Simplifying
x + -5 = 9.273618495

Reorder the terms:
-5 + x = 9.273618495

Solving
-5 + x = 9.273618495

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 = 9.273618495 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.273618495 + 5
x = 9.273618495 + 5

Combine like terms: 9.273618495 + 5 = 14.273618495
x = 14.273618495

Simplifying
x = 14.273618495


Subproblem 2
x + -5 = -9.273618495

Simplifying
x + -5 = -9.273618495

Reorder the terms:
-5 + x = -9.273618495

Solving
-5 + x = -9.273618495

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 = -9.273618495 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.273618495 + 5
x = -9.273618495 + 5

Combine like terms: -9.273618495 + 5 = -4.273618495
x = -4.273618495

Simplifying
x = -4.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.273618495, -4.273618495}

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