2x+x(2x+30)=180

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Solution for 2x+x(2x+30)=180 equation: 


Simplifying
2x + x(2x + 30) = 180

Reorder the terms:
2x + x(30 + 2x) = 180
2x + (30 * x + 2x * x) = 180
2x + (30x + 2x2) = 180

Combine like terms: 2x + 30x = 32x
32x + 2x2 = 180

Solving
32x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 32x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 32x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 16x + x2 = 0

Solving
-90 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 16x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 16x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 16x + x2 = 0 + 90
16x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
16x + x2 = 90

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 90 + 64

Reorder the terms:
64 + 16x + x2 = 90 + 64

Combine like terms: 90 + 64 = 154
64 + 16x + x2 = 154

Factor a perfect square on the left side:
(x + 8)(x + 8) = 154

Calculate the square root of the right side: 12.409673646

Break this problem into two subproblems by setting 
(x + 8) equal to 12.409673646 and -12.409673646.


Subproblem 1
x + 8 = 12.409673646

Simplifying
x + 8 = 12.409673646

Reorder the terms:
8 + x = 12.409673646

Solving
8 + x = 12.409673646

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 12.409673646 + -8

Combine like terms: 8 + -8 = 0
0 + x = 12.409673646 + -8
x = 12.409673646 + -8

Combine like terms: 12.409673646 + -8 = 4.409673646
x = 4.409673646

Simplifying
x = 4.409673646


Subproblem 2
x + 8 = -12.409673646

Simplifying
x + 8 = -12.409673646

Reorder the terms:
8 + x = -12.409673646

Solving
8 + x = -12.409673646

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -12.409673646 + -8

Combine like terms: 8 + -8 = 0
0 + x = -12.409673646 + -8
x = -12.409673646 + -8

Combine like terms: -12.409673646 + -8 = -20.409673646
x = -20.409673646

Simplifying
x = -20.409673646


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.409673646, -20.409673646}
Solution
x = {4.409673646, -20.409673646}

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