2x*2x-2x-180=0

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Solution for 2x*2x-2x-180=0 equation: 


Simplifying
2x * 2x + -2x + -180 = 0

Reorder the terms for easier multiplication:
2 * 2x * x + -2x + -180 = 0

Multiply 2 * 2
4x * x + -2x + -180 = 0

Multiply x * x
4x2 + -2x + -180 = 0

Reorder the terms:
-180 + -2x + 4x2 = 0

Solving
-180 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + -1x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
-90 + -1x + 2x2 = 0

Solving
-90 + -1x + 2x2 = 0

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

Divide each side by '2'.
-45 + -0.5x + x2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -0.5x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -0.5x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -0.5x + x2 = 0 + 45
-0.5x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-0.5x + x2 = 45

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 45 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 45 + 0.0625

Combine like terms: 45 + 0.0625 = 45.0625
0.0625 + -0.5x + x2 = 45.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 45.0625

Calculate the square root of the right side: 6.712860791

Break this problem into two subproblems by setting 
(x + -0.25) equal to 6.712860791 and -6.712860791.


Subproblem 1
x + -0.25 = 6.712860791

Simplifying
x + -0.25 = 6.712860791

Reorder the terms:
-0.25 + x = 6.712860791

Solving
-0.25 + x = 6.712860791

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 6.712860791 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 6.712860791 + 0.25
x = 6.712860791 + 0.25

Combine like terms: 6.712860791 + 0.25 = 6.962860791
x = 6.962860791

Simplifying
x = 6.962860791


Subproblem 2
x + -0.25 = -6.712860791

Simplifying
x + -0.25 = -6.712860791

Reorder the terms:
-0.25 + x = -6.712860791

Solving
-0.25 + x = -6.712860791

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -6.712860791 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -6.712860791 + 0.25
x = -6.712860791 + 0.25

Combine like terms: -6.712860791 + 0.25 = -6.462860791
x = -6.462860791

Simplifying
x = -6.462860791


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.962860791, -6.462860791}
Solution
x = {6.962860791, -6.462860791}

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