x(x+10)=40

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Solution for x(x+10)=40 equation: 


Simplifying
x(x + 10) = 40

Reorder the terms:
x(10 + x) = 40
(10 * x + x * x) = 40
(10x + x2) = 40

Solving
10x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 10x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 10x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 10x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 10x + x2 = 0 + 40
10x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
10x + x2 = 40

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 = 40 + 25

Reorder the terms:
25 + 10x + x2 = 40 + 25

Combine like terms: 40 + 25 = 65
25 + 10x + x2 = 65

Factor a perfect square on the left side:
(x + 5)(x + 5) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + 5) equal to 8.062257748 and -8.062257748.


Subproblem 1
x + 5 = 8.062257748

Simplifying
x + 5 = 8.062257748

Reorder the terms:
5 + x = 8.062257748

Solving
5 + x = 8.062257748

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 = 8.062257748 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.062257748 + -5
x = 8.062257748 + -5

Combine like terms: 8.062257748 + -5 = 3.062257748
x = 3.062257748

Simplifying
x = 3.062257748


Subproblem 2
x + 5 = -8.062257748

Simplifying
x + 5 = -8.062257748

Reorder the terms:
5 + x = -8.062257748

Solving
5 + x = -8.062257748

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 = -8.062257748 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.062257748 + -5
x = -8.062257748 + -5

Combine like terms: -8.062257748 + -5 = -13.062257748
x = -13.062257748

Simplifying
x = -13.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.062257748, -13.062257748}

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