6x^2-4x+5x-10=0

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Solution for 6x^2-4x+5x-10=0 equation: 


Simplifying
6x2 + -4x + 5x + -10 = 0

Reorder the terms:
-10 + -4x + 5x + 6x2 = 0

Combine like terms: -4x + 5x = 1x
-10 + 1x + 6x2 = 0

Solving
-10 + 1x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-1.666666667 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.1666666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.1666666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.1666666667x + x2 = 0 + 1.666666667
0.1666666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.1666666667x + x2 = 1.666666667

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 1.666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 1.666666667 + 0.006944444447

Combine like terms: 1.666666667 + 0.006944444447 = 1.673611111447
0.006944444447 + 0.1666666667x + x2 = 1.673611111447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 1.673611111447

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 1.293681225 and -1.293681225.


Subproblem 1
x + 0.08333333335 = 1.293681225

Simplifying
x + 0.08333333335 = 1.293681225

Reorder the terms:
0.08333333335 + x = 1.293681225

Solving
0.08333333335 + x = 1.293681225

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 1.293681225 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 1.293681225 + -0.08333333335
x = 1.293681225 + -0.08333333335

Combine like terms: 1.293681225 + -0.08333333335 = 1.21034789165
x = 1.21034789165

Simplifying
x = 1.21034789165


Subproblem 2
x + 0.08333333335 = -1.293681225

Simplifying
x + 0.08333333335 = -1.293681225

Reorder the terms:
0.08333333335 + x = -1.293681225

Solving
0.08333333335 + x = -1.293681225

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -1.293681225 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -1.293681225 + -0.08333333335
x = -1.293681225 + -0.08333333335

Combine like terms: -1.293681225 + -0.08333333335 = -1.37701455835
x = -1.37701455835

Simplifying
x = -1.37701455835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.21034789165, -1.37701455835}

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