18x^2-45x-50=10

Solution for 18x^2-45x-50=10 equation:

Simplifying
18x2 + -45x + -50 = 10

Reorder the terms:
-50 + -45x + 18x2 = 10

Solving
-50 + -45x + 18x2 = 10

Solving for variable 'x'.

Reorder the terms:
-50 + -10 + -45x + 18x2 = 10 + -10

Combine like terms: -50 + -10 = -60
-60 + -45x + 18x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-60 + -45x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -15x + 6x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-20 + -15x + 6x2)' equal to zero and attempt to solve:

Simplifying
-20 + -15x + 6x2 = 0

Solving
-20 + -15x + 6x2 = 0

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

Divide each side by '6'.
-3.333333333 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -2.5x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -2.5x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -2.5x + x2 = 0 + 3.333333333
-2.5x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-2.5x + x2 = 3.333333333

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3.333333333 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3.333333333 + 1.5625

Combine like terms: 3.333333333 + 1.5625 = 4.895833333
1.5625 + -2.5x + x2 = 4.895833333

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 4.895833333

Calculate the square root of the right side: 2.212653008

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.212653008 and -2.212653008.

Subproblem 1
x + -1.25 = 2.212653008

Simplifying
x + -1.25 = 2.212653008

Reorder the terms:
-1.25 + x = 2.212653008

Solving
-1.25 + x = 2.212653008

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.212653008 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.212653008 + 1.25
x = 2.212653008 + 1.25

Combine like terms: 2.212653008 + 1.25 = 3.462653008
x = 3.462653008

Simplifying
x = 3.462653008

Subproblem 2
x + -1.25 = -2.212653008

Simplifying
x + -1.25 = -2.212653008

Reorder the terms:
-1.25 + x = -2.212653008

Solving
-1.25 + x = -2.212653008

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.212653008 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.212653008 + 1.25
x = -2.212653008 + 1.25

Combine like terms: -2.212653008 + 1.25 = -0.962653008
x = -0.962653008

Simplifying
x = -0.962653008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.462653008, -0.962653008}
Solution
x = {3.462653008, -0.962653008}