-31=(x^2)+10x-5

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Solution for -31=(x^2)+10x-5 equation: 


Simplifying
-31 = (x2) + 10x + -5
-31 = x2 + 10x + -5

Reorder the terms:
-31 = -5 + 10x + x2

Solving
-31 = -5 + 10x + x2

Solving for variable 'x'.

Combine like terms: -31 + 5 = -26
-26 + -10x + -1x2 = -5 + 10x + x2 + 5 + -10x + -1x2

Reorder the terms:
-26 + -10x + -1x2 = -5 + 5 + 10x + -10x + x2 + -1x2

Combine like terms: -5 + 5 = 0
-26 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-26 + -10x + -1x2 = 10x + -10x + x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(26 + 10x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(26 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
26 + 10x + x2 = 0

Solving
26 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + 10x + -26 + x2 = 0 + -26

Reorder the terms:
26 + -26 + 10x + x2 = 0 + -26

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

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

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -26 + 25

Reorder the terms:
25 + 10x + x2 = -26 + 25

Combine like terms: -26 + 25 = -1
25 + 10x + x2 = -1

Factor a perfect square on the left side:
(x + 5)(x + 5) = -1

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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