2x(x+5)-3x=x+18

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Solution for 2x(x+5)-3x=x+18 equation: 


Simplifying
2x(x + 5) + -3x = x + 18

Reorder the terms:
2x(5 + x) + -3x = x + 18
(5 * 2x + x * 2x) + -3x = x + 18
(10x + 2x2) + -3x = x + 18

Reorder the terms:
10x + -3x + 2x2 = x + 18

Combine like terms: 10x + -3x = 7x
7x + 2x2 = x + 18

Reorder the terms:
7x + 2x2 = 18 + x

Solving
7x + 2x2 = 18 + x

Solving for variable 'x'.

Reorder the terms:
-18 + 7x + -1x + 2x2 = 18 + x + -18 + -1x

Combine like terms: 7x + -1x = 6x
-18 + 6x + 2x2 = 18 + x + -18 + -1x

Reorder the terms:
-18 + 6x + 2x2 = 18 + -18 + x + -1x

Combine like terms: 18 + -18 = 0
-18 + 6x + 2x2 = 0 + x + -1x
-18 + 6x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-18 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 3x + x2 = 0

Solving
-9 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 3x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 3x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3x + x2 = 0 + 9
3x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
3x + x2 = 9

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 9 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + 3x + x2 = 11.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 1.5 = 3.354101966

Simplifying
x + 1.5 = 3.354101966

Reorder the terms:
1.5 + x = 3.354101966

Solving
1.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.354101966 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.354101966 + -1.5
x = 3.354101966 + -1.5

Combine like terms: 3.354101966 + -1.5 = 1.854101966
x = 1.854101966

Simplifying
x = 1.854101966


Subproblem 2
x + 1.5 = -3.354101966

Simplifying
x + 1.5 = -3.354101966

Reorder the terms:
1.5 + x = -3.354101966

Solving
1.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.354101966 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.354101966 + -1.5
x = -3.354101966 + -1.5

Combine like terms: -3.354101966 + -1.5 = -4.854101966
x = -4.854101966

Simplifying
x = -4.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.854101966, -4.854101966}
Solution
x = {1.854101966, -4.854101966}

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