x^2-10x-64=0

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Solution for x^2-10x-64=0 equation: 


Simplifying
x2 + -10x + -64 = 0

Reorder the terms:
-64 + -10x + x2 = 0

Solving
-64 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -10x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + -10x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -10x + x2 = 0 + 64
-10x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
-10x + x2 = 64

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 = 64 + 25

Reorder the terms:
25 + -10x + x2 = 64 + 25

Combine like terms: 64 + 25 = 89
25 + -10x + x2 = 89

Factor a perfect square on the left side:
(x + -5)(x + -5) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -5) equal to 9.433981132 and -9.433981132.


Subproblem 1
x + -5 = 9.433981132

Simplifying
x + -5 = 9.433981132

Reorder the terms:
-5 + x = 9.433981132

Solving
-5 + x = 9.433981132

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 = 9.433981132 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.433981132 + 5
x = 9.433981132 + 5

Combine like terms: 9.433981132 + 5 = 14.433981132
x = 14.433981132

Simplifying
x = 14.433981132


Subproblem 2
x + -5 = -9.433981132

Simplifying
x + -5 = -9.433981132

Reorder the terms:
-5 + x = -9.433981132

Solving
-5 + x = -9.433981132

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 = -9.433981132 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.433981132 + 5
x = -9.433981132 + 5

Combine like terms: -9.433981132 + 5 = -4.433981132
x = -4.433981132

Simplifying
x = -4.433981132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.433981132, -4.433981132}

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