(x+9)*2x=24

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Solution for (x+9)*2x=24 equation:


Simplifying
(x + 9) * 2x = 24

Reorder the terms:
(9 + x) * 2x = 24

Reorder the terms for easier multiplication:
2x(9 + x) = 24
(9 * 2x + x * 2x) = 24
(18x + 2x2) = 24

Solving
18x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 18x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 9x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-12 + 9x + x2 = 0

Solving
-12 + 9x + x2 = 0

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 = 32.25
20.25 + 9x + x2 = 32.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 4.5 = 5.678908346

Simplifying
x + 4.5 = 5.678908346

Reorder the terms:
4.5 + x = 5.678908346

Solving
4.5 + x = 5.678908346

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 = 5.678908346 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.678908346 + -4.5
x = 5.678908346 + -4.5

Combine like terms: 5.678908346 + -4.5 = 1.178908346
x = 1.178908346

Simplifying
x = 1.178908346


Subproblem 2
x + 4.5 = -5.678908346

Simplifying
x + 4.5 = -5.678908346

Reorder the terms:
4.5 + x = -5.678908346

Solving
4.5 + x = -5.678908346

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 = -5.678908346 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.678908346 + -4.5
x = -5.678908346 + -4.5

Combine like terms: -5.678908346 + -4.5 = -10.178908346
x = -10.178908346

Simplifying
x = -10.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.178908346, -10.178908346}
Solution
x = {1.178908346, -10.178908346}

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