6x^2-x-90=

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Solution for 6x^2-x-90= equation: 


Simplifying
6x2 + -1x + -90 = 0

Reorder the terms:
-90 + -1x + 6x2 = 0

Solving
-90 + -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'.
-15 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -0.1666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -0.1666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -0.1666666667x + x2 = 0 + 15
-0.1666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-0.1666666667x + x2 = 15

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 = 15 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 15 + 0.006944444447

Combine like terms: 15 + 0.006944444447 = 15.006944444447
0.006944444447 + -0.1666666667x + x2 = 15.006944444447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 15.006944444447

Calculate the square root of the right side: 3.873879766

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 3.873879766 and -3.873879766.


Subproblem 1
x + -0.08333333335 = 3.873879766

Simplifying
x + -0.08333333335 = 3.873879766

Reorder the terms:
-0.08333333335 + x = 3.873879766

Solving
-0.08333333335 + x = 3.873879766

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 = 3.873879766 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 3.873879766 + 0.08333333335
x = 3.873879766 + 0.08333333335

Combine like terms: 3.873879766 + 0.08333333335 = 3.95721309935
x = 3.95721309935

Simplifying
x = 3.95721309935


Subproblem 2
x + -0.08333333335 = -3.873879766

Simplifying
x + -0.08333333335 = -3.873879766

Reorder the terms:
-0.08333333335 + x = -3.873879766

Solving
-0.08333333335 + x = -3.873879766

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 = -3.873879766 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -3.873879766 + 0.08333333335
x = -3.873879766 + 0.08333333335

Combine like terms: -3.873879766 + 0.08333333335 = -3.79054643265
x = -3.79054643265

Simplifying
x = -3.79054643265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.95721309935, -3.79054643265}

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