6x^2-9x=18x^2-10x-26

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Solution for 6x^2-9x=18x^2-10x-26 equation: 


Simplifying
6x2 + -9x = 18x2 + -10x + -26

Reorder the terms:
-9x + 6x2 = 18x2 + -10x + -26

Reorder the terms:
-9x + 6x2 = -26 + -10x + 18x2

Solving
-9x + 6x2 = -26 + -10x + 18x2

Solving for variable 'x'.

Reorder the terms:
26 + -9x + 10x + 6x2 + -18x2 = -26 + -10x + 18x2 + 26 + 10x + -18x2

Combine like terms: -9x + 10x = 1x
26 + 1x + 6x2 + -18x2 = -26 + -10x + 18x2 + 26 + 10x + -18x2

Combine like terms: 6x2 + -18x2 = -12x2
26 + 1x + -12x2 = -26 + -10x + 18x2 + 26 + 10x + -18x2

Reorder the terms:
26 + 1x + -12x2 = -26 + 26 + -10x + 10x + 18x2 + -18x2

Combine like terms: -26 + 26 = 0
26 + 1x + -12x2 = 0 + -10x + 10x + 18x2 + -18x2
26 + 1x + -12x2 = -10x + 10x + 18x2 + -18x2

Combine like terms: -10x + 10x = 0
26 + 1x + -12x2 = 0 + 18x2 + -18x2
26 + 1x + -12x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
26 + 1x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-2.166666667 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + -0.08333333333x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + -0.08333333333x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + -0.08333333333x + x2 = 0 + 2.166666667
-0.08333333333x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
-0.08333333333x + x2 = 2.166666667

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 2.166666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 2.166666667 + 0.001736111111

Combine like terms: 2.166666667 + 0.001736111111 = 2.168402778111
0.001736111111 + -0.08333333333x + x2 = 2.168402778111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 2.168402778111

Calculate the square root of the right side: 1.472549754

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 1.472549754 and -1.472549754.


Subproblem 1
x + -0.04166666667 = 1.472549754

Simplifying
x + -0.04166666667 = 1.472549754

Reorder the terms:
-0.04166666667 + x = 1.472549754

Solving
-0.04166666667 + x = 1.472549754

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 1.472549754 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 1.472549754 + 0.04166666667
x = 1.472549754 + 0.04166666667

Combine like terms: 1.472549754 + 0.04166666667 = 1.51421642067
x = 1.51421642067

Simplifying
x = 1.51421642067


Subproblem 2
x + -0.04166666667 = -1.472549754

Simplifying
x + -0.04166666667 = -1.472549754

Reorder the terms:
-0.04166666667 + x = -1.472549754

Solving
-0.04166666667 + x = -1.472549754

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -1.472549754 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -1.472549754 + 0.04166666667
x = -1.472549754 + 0.04166666667

Combine like terms: -1.472549754 + 0.04166666667 = -1.43088308733
x = -1.43088308733

Simplifying
x = -1.43088308733


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.51421642067, -1.43088308733}

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