x^2+3x-31=0

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Solution for x^2+3x-31=0 equation: 


Simplifying
x2 + 3x + -31 = 0

Reorder the terms:
-31 + 3x + x2 = 0

Solving
-31 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 3x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 3x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 3x + x2 = 0 + 31
3x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
3x + x2 = 31

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 31 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 31 + 2.25

Combine like terms: 31 + 2.25 = 33.25
2.25 + 3x + x2 = 33.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.766281297 and -5.766281297.


Subproblem 1
x + 1.5 = 5.766281297

Simplifying
x + 1.5 = 5.766281297

Reorder the terms:
1.5 + x = 5.766281297

Solving
1.5 + x = 5.766281297

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 5.766281297 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.766281297 + -1.5
x = 5.766281297 + -1.5

Combine like terms: 5.766281297 + -1.5 = 4.266281297
x = 4.266281297

Simplifying
x = 4.266281297


Subproblem 2
x + 1.5 = -5.766281297

Simplifying
x + 1.5 = -5.766281297

Reorder the terms:
1.5 + x = -5.766281297

Solving
1.5 + x = -5.766281297

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -5.766281297 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.766281297 + -1.5
x = -5.766281297 + -1.5

Combine like terms: -5.766281297 + -1.5 = -7.266281297
x = -7.266281297

Simplifying
x = -7.266281297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.266281297, -7.266281297}

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