5x(2x-2)=180

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Solution for 5x(2x-2)=180 equation: 


Simplifying
5x(2x + -2) = 180

Reorder the terms:
5x(-2 + 2x) = 180
(-2 * 5x + 2x * 5x) = 180
(-10x + 10x2) = 180

Solving
-10x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -10x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -10x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + -1x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-18 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + -1x + x2 = 0

Solving
-18 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -1x + x2 = 0 + 18

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 18 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + -1x + x2 = 18.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + -0.5 = 4.272001873

Simplifying
x + -0.5 = 4.272001873

Reorder the terms:
-0.5 + x = 4.272001873

Solving
-0.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 4.272001873 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4.272001873 + 0.5
x = 4.272001873 + 0.5

Combine like terms: 4.272001873 + 0.5 = 4.772001873
x = 4.772001873

Simplifying
x = 4.772001873


Subproblem 2
x + -0.5 = -4.272001873

Simplifying
x + -0.5 = -4.272001873

Reorder the terms:
-0.5 + x = -4.272001873

Solving
-0.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -4.272001873 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4.272001873 + 0.5
x = -4.272001873 + 0.5

Combine like terms: -4.272001873 + 0.5 = -3.772001873
x = -3.772001873

Simplifying
x = -3.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.772001873, -3.772001873}
Solution
x = {4.772001873, -3.772001873}

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