720=(2x-2)(x)

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Solution for 720=(2x-2)(x) equation: 


Simplifying
720 = (2x + -2)(x)

Reorder the terms:
720 = (-2 + 2x)(x)

Reorder the terms for easier multiplication:
720 = x(-2 + 2x)
720 = (-2 * x + 2x * x)
720 = (-2x + 2x2)

Solving
720 = -2x + 2x2

Solving for variable 'x'.

Reorder the terms:
720 + 2x + -2x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
720 + 2x + -2x2 = 0 + 2x2 + -2x2
720 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
720 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(360 + x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(360 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
360 + x + -1x2 = 0

Solving
360 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-360 + -1x + x2 = 0

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + -1x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + -1x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + -1x + x2 = 0 + 360
-1x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
-1x + x2 = 360

The x term is x.  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 = 360 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 360 + 0.25

Combine like terms: 360 + 0.25 = 360.25
0.25 + -1x + x2 = 360.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 360.25

Calculate the square root of the right side: 18.980252896

Break this problem into two subproblems by setting 
(x + 0.5) equal to 18.980252896 and -18.980252896.


Subproblem 1
x + 0.5 = 18.980252896

Simplifying
x + 0.5 = 18.980252896

Reorder the terms:
0.5 + x = 18.980252896

Solving
0.5 + x = 18.980252896

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 = 18.980252896 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 18.980252896 + -0.5
x = 18.980252896 + -0.5

Combine like terms: 18.980252896 + -0.5 = 18.480252896
x = 18.480252896

Simplifying
x = 18.480252896


Subproblem 2
x + 0.5 = -18.980252896

Simplifying
x + 0.5 = -18.980252896

Reorder the terms:
0.5 + x = -18.980252896

Solving
0.5 + x = -18.980252896

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 = -18.980252896 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -18.980252896 + -0.5
x = -18.980252896 + -0.5

Combine like terms: -18.980252896 + -0.5 = -19.480252896
x = -19.480252896

Simplifying
x = -19.480252896


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.480252896, -19.480252896}
Solution
x = {18.480252896, -19.480252896}

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