x(x-9)+12=0

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Solution for x(x-9)+12=0 equation: 


Simplifying
x(x + -9) + 12 = 0

Reorder the terms:
x(-9 + x) + 12 = 0
(-9 * x + x * x) + 12 = 0
(-9x + x2) + 12 = 0

Reorder the terms:
12 + -9x + x2 = 0

Solving
12 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -9x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -9x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -9x + x2 = 0 + -12
-9x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-9x + x2 = -12

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -12 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -12 + 20.25

Combine like terms: -12 + 20.25 = 8.25
20.25 + -9x + x2 = 8.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + -4.5 = 2.872281323

Simplifying
x + -4.5 = 2.872281323

Reorder the terms:
-4.5 + x = 2.872281323

Solving
-4.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 2.872281323 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 2.872281323 + 4.5
x = 2.872281323 + 4.5

Combine like terms: 2.872281323 + 4.5 = 7.372281323
x = 7.372281323

Simplifying
x = 7.372281323


Subproblem 2
x + -4.5 = -2.872281323

Simplifying
x + -4.5 = -2.872281323

Reorder the terms:
-4.5 + x = -2.872281323

Solving
-4.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -2.872281323 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -2.872281323 + 4.5
x = -2.872281323 + 4.5

Combine like terms: -2.872281323 + 4.5 = 1.627718677
x = 1.627718677

Simplifying
x = 1.627718677


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.372281323, 1.627718677}

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