-5x^2-31x-72=0

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Solution for -5x^2-31x-72=0 equation: 


Simplifying
-5x2 + -31x + -72 = 0

Reorder the terms:
-72 + -31x + -5x2 = 0

Solving
-72 + -31x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(72 + 31x + 5x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(72 + 31x + 5x2)' equal to zero and attempt to solve:

Simplifying
72 + 31x + 5x2 = 0

Solving
72 + 31x + 5x2 = 0

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

Divide each side by '5'.
14.4 + 6.2x + x2 = 0

Move the constant term to the right:

Add '-14.4' to each side of the equation.
14.4 + 6.2x + -14.4 + x2 = 0 + -14.4

Reorder the terms:
14.4 + -14.4 + 6.2x + x2 = 0 + -14.4

Combine like terms: 14.4 + -14.4 = 0.0
0.0 + 6.2x + x2 = 0 + -14.4
6.2x + x2 = 0 + -14.4

Combine like terms: 0 + -14.4 = -14.4
6.2x + x2 = -14.4

The x term is 6.2x.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2x + 9.61 + x2 = -14.4 + 9.61

Reorder the terms:
9.61 + 6.2x + x2 = -14.4 + 9.61

Combine like terms: -14.4 + 9.61 = -4.79
9.61 + 6.2x + x2 = -4.79

Factor a perfect square on the left side:
(x + 3.1)(x + 3.1) = -4.79

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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