2x(2x+4)=180

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Solution for 2x(2x+4)=180 equation: 


Simplifying
2x(2x + 4) = 180

Reorder the terms:
2x(4 + 2x) = 180
(4 * 2x + 2x * 2x) = 180
(8x + 4x2) = 180

Solving
8x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 8x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 2x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 2x + x2 = 0

Solving
-45 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 2x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 2x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2x + x2 = 0 + 45
2x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
2x + x2 = 45

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 45 + 1

Reorder the terms:
1 + 2x + x2 = 45 + 1

Combine like terms: 45 + 1 = 46
1 + 2x + x2 = 46

Factor a perfect square on the left side:
(x + 1)(x + 1) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 1) equal to 6.782329983 and -6.782329983.


Subproblem 1
x + 1 = 6.782329983

Simplifying
x + 1 = 6.782329983

Reorder the terms:
1 + x = 6.782329983

Solving
1 + x = 6.782329983

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.782329983 + -1
x = 6.782329983 + -1

Combine like terms: 6.782329983 + -1 = 5.782329983
x = 5.782329983

Simplifying
x = 5.782329983


Subproblem 2
x + 1 = -6.782329983

Simplifying
x + 1 = -6.782329983

Reorder the terms:
1 + x = -6.782329983

Solving
1 + x = -6.782329983

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.782329983 + -1
x = -6.782329983 + -1

Combine like terms: -6.782329983 + -1 = -7.782329983
x = -7.782329983

Simplifying
x = -7.782329983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.782329983, -7.782329983}
Solution
x = {5.782329983, -7.782329983}

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