180x^2-180x-1410=0

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Solution for 180x^2-180x-1410=0 equation: 


Simplifying
180x2 + -180x + -1410 = 0

Reorder the terms:
-1410 + -180x + 180x2 = 0

Solving
-1410 + -180x + 180x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(-47 + -6x + 6x2) = 0

Ignore the factor 30.

Subproblem 1
Set the factor '(-47 + -6x + 6x2)' equal to zero and attempt to solve:

Simplifying
-47 + -6x + 6x2 = 0

Solving
-47 + -6x + 6x2 = 0

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

Divide each side by '6'.
-7.833333333 + -1x + x2 = 0

Move the constant term to the right:

Add '7.833333333' to each side of the equation.
-7.833333333 + -1x + 7.833333333 + x2 = 0 + 7.833333333

Reorder the terms:
-7.833333333 + 7.833333333 + -1x + x2 = 0 + 7.833333333

Combine like terms: -7.833333333 + 7.833333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 7.833333333
-1x + x2 = 0 + 7.833333333

Combine like terms: 0 + 7.833333333 = 7.833333333
-1x + x2 = 7.833333333

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 = 7.833333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 7.833333333 + 0.25

Combine like terms: 7.833333333 + 0.25 = 8.083333333
0.25 + -1x + x2 = 8.083333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 8.083333333

Calculate the square root of the right side: 2.843120351

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.843120351 and -2.843120351.


Subproblem 1
x + -0.5 = 2.843120351

Simplifying
x + -0.5 = 2.843120351

Reorder the terms:
-0.5 + x = 2.843120351

Solving
-0.5 + x = 2.843120351

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 = 2.843120351 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.843120351 + 0.5
x = 2.843120351 + 0.5

Combine like terms: 2.843120351 + 0.5 = 3.343120351
x = 3.343120351

Simplifying
x = 3.343120351


Subproblem 2
x + -0.5 = -2.843120351

Simplifying
x + -0.5 = -2.843120351

Reorder the terms:
-0.5 + x = -2.843120351

Solving
-0.5 + x = -2.843120351

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 = -2.843120351 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.843120351 + 0.5
x = -2.843120351 + 0.5

Combine like terms: -2.843120351 + 0.5 = -2.343120351
x = -2.343120351

Simplifying
x = -2.343120351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.343120351, -2.343120351}
Solution
x = {3.343120351, -2.343120351}

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