10x^2-180x-90=0

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Solution for 10x^2-180x-90=0 equation: 


Simplifying
10x2 + -180x + -90 = 0

Reorder the terms:
-90 + -180x + 10x2 = 0

Solving
-90 + -180x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-9 + -18x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-9 + -18x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -18x + x2 = 0

Solving
-9 + -18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -18x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -18x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -18x + x2 = 0 + 9
-18x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-18x + x2 = 9

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = 9 + 81

Reorder the terms:
81 + -18x + x2 = 9 + 81

Combine like terms: 9 + 81 = 90
81 + -18x + x2 = 90

Factor a perfect square on the left side:
(x + -9)(x + -9) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(x + -9) equal to 9.486832981 and -9.486832981.


Subproblem 1
x + -9 = 9.486832981

Simplifying
x + -9 = 9.486832981

Reorder the terms:
-9 + x = 9.486832981

Solving
-9 + x = 9.486832981

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 9.486832981 + 9

Combine like terms: -9 + 9 = 0
0 + x = 9.486832981 + 9
x = 9.486832981 + 9

Combine like terms: 9.486832981 + 9 = 18.486832981
x = 18.486832981

Simplifying
x = 18.486832981


Subproblem 2
x + -9 = -9.486832981

Simplifying
x + -9 = -9.486832981

Reorder the terms:
-9 + x = -9.486832981

Solving
-9 + x = -9.486832981

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -9.486832981 + 9

Combine like terms: -9 + 9 = 0
0 + x = -9.486832981 + 9
x = -9.486832981 + 9

Combine like terms: -9.486832981 + 9 = -0.486832981
x = -0.486832981

Simplifying
x = -0.486832981


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.486832981, -0.486832981}
Solution
x = {18.486832981, -0.486832981}

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