x(x+5)=12

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Solution for x(x+5)=12 equation:


Simplifying
x(x + 5) = 12

Reorder the terms:
x(5 + x) = 12
(5 * x + x * x) = 12
(5x + x2) = 12

Solving
5x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 5x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 5x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 5x + x2 = 0 + 12
5x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
5x + x2 = 12

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 12 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 12 + 6.25

Combine like terms: 12 + 6.25 = 18.25
6.25 + 5x + x2 = 18.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 2.5 = 4.272001873

Simplifying
x + 2.5 = 4.272001873

Reorder the terms:
2.5 + x = 4.272001873

Solving
2.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.272001873 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.272001873 + -2.5
x = 4.272001873 + -2.5

Combine like terms: 4.272001873 + -2.5 = 1.772001873
x = 1.772001873

Simplifying
x = 1.772001873


Subproblem 2
x + 2.5 = -4.272001873

Simplifying
x + 2.5 = -4.272001873

Reorder the terms:
2.5 + x = -4.272001873

Solving
2.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.272001873 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.272001873 + -2.5
x = -4.272001873 + -2.5

Combine like terms: -4.272001873 + -2.5 = -6.772001873
x = -6.772001873

Simplifying
x = -6.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.772001873, -6.772001873}

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