x(x+4)=36

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Solution for x(x+4)=36 equation: 


Simplifying
x(x + 4) = 36

Reorder the terms:
x(4 + x) = 36
(4 * x + x * x) = 36
(4x + x2) = 36

Solving
4x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + 4x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 4x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 4x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4x + x2 = 0 + 36
4x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
4x + x2 = 36

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 36 + 4

Reorder the terms:
4 + 4x + x2 = 36 + 4

Combine like terms: 36 + 4 = 40
4 + 4x + x2 = 40

Factor a perfect square on the left side:
(x + 2)(x + 2) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + 2) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + 2 = 6.32455532

Simplifying
x + 2 = 6.32455532

Reorder the terms:
2 + x = 6.32455532

Solving
2 + x = 6.32455532

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.32455532 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.32455532 + -2
x = 6.32455532 + -2

Combine like terms: 6.32455532 + -2 = 4.32455532
x = 4.32455532

Simplifying
x = 4.32455532


Subproblem 2
x + 2 = -6.32455532

Simplifying
x + 2 = -6.32455532

Reorder the terms:
2 + x = -6.32455532

Solving
2 + x = -6.32455532

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.32455532 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.32455532 + -2
x = -6.32455532 + -2

Combine like terms: -6.32455532 + -2 = -8.32455532
x = -8.32455532

Simplifying
x = -8.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.32455532, -8.32455532}

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