x(x+10)=64

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Solution for x(x+10)=64 equation: 


Simplifying
x(x + 10) = 64

Reorder the terms:
x(10 + x) = 64
(10 * x + x * x) = 64
(10x + x2) = 64

Solving
10x + x2 = 64

Solving for variable 'x'.

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

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

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 = 4.433981132
x = 4.433981132

Simplifying
x = 4.433981132


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 = -14.433981132
x = -14.433981132

Simplifying
x = -14.433981132


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

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