(x+8)(x)=40

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Solution for (x+8)(x)=40 equation: 


Simplifying
(x + 8)(x) = 40

Reorder the terms:
(8 + x)(x) = 40

Reorder the terms for easier multiplication:
x(8 + x) = 40
(8 * x + x * x) = 40
(8x + x2) = 40

Solving
8x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 8x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 8x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + 8x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 8x + x2 = 0 + 40
8x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
8x + x2 = 40

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 40 + 16

Reorder the terms:
16 + 8x + x2 = 40 + 16

Combine like terms: 40 + 16 = 56
16 + 8x + x2 = 56

Factor a perfect square on the left side:
(x + 4)(x + 4) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 4) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + 4 = 7.483314774

Simplifying
x + 4 = 7.483314774

Reorder the terms:
4 + x = 7.483314774

Solving
4 + x = 7.483314774

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.483314774 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.483314774 + -4
x = 7.483314774 + -4

Combine like terms: 7.483314774 + -4 = 3.483314774
x = 3.483314774

Simplifying
x = 3.483314774


Subproblem 2
x + 4 = -7.483314774

Simplifying
x + 4 = -7.483314774

Reorder the terms:
4 + x = -7.483314774

Solving
4 + x = -7.483314774

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.483314774 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.483314774 + -4
x = -7.483314774 + -4

Combine like terms: -7.483314774 + -4 = -11.483314774
x = -11.483314774

Simplifying
x = -11.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.483314774, -11.483314774}

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