-5x^2-x=x^2-9x+31

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Solution for -5x^2-x=x^2-9x+31 equation: 


Simplifying
-5x2 + -1x = x2 + -9x + 31

Reorder the terms:
-1x + -5x2 = x2 + -9x + 31

Reorder the terms:
-1x + -5x2 = 31 + -9x + x2

Solving
-1x + -5x2 = 31 + -9x + x2

Solving for variable 'x'.

Reorder the terms:
-31 + -1x + 9x + -5x2 + -1x2 = 31 + -9x + x2 + -31 + 9x + -1x2

Combine like terms: -1x + 9x = 8x
-31 + 8x + -5x2 + -1x2 = 31 + -9x + x2 + -31 + 9x + -1x2

Combine like terms: -5x2 + -1x2 = -6x2
-31 + 8x + -6x2 = 31 + -9x + x2 + -31 + 9x + -1x2

Reorder the terms:
-31 + 8x + -6x2 = 31 + -31 + -9x + 9x + x2 + -1x2

Combine like terms: 31 + -31 = 0
-31 + 8x + -6x2 = 0 + -9x + 9x + x2 + -1x2
-31 + 8x + -6x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
-31 + 8x + -6x2 = 0 + x2 + -1x2
-31 + 8x + -6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-31 + 8x + -6x2 = 0

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

Divide each side by '-6'.
5.166666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-5.166666667' to each side of the equation.
5.166666667 + -1.333333333x + -5.166666667 + x2 = 0 + -5.166666667

Reorder the terms:
5.166666667 + -5.166666667 + -1.333333333x + x2 = 0 + -5.166666667

Combine like terms: 5.166666667 + -5.166666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -5.166666667
-1.333333333x + x2 = 0 + -5.166666667

Combine like terms: 0 + -5.166666667 = -5.166666667
-1.333333333x + x2 = -5.166666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -5.166666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -5.166666667 + 0.4444444442

Combine like terms: -5.166666667 + 0.4444444442 = -4.7222222228
0.4444444442 + -1.333333333x + x2 = -4.7222222228

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -4.7222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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