x^2+5x-31=0

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


Simplifying
x2 + 5x + -31 = 0

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

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

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

Combine like terms: -31 + 31 = 0
0 + 5x + x2 = 0 + 31
5x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
5x + x2 = 31

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 31 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 31 + 6.25

Combine like terms: 31 + 6.25 = 37.25
6.25 + 5x + x2 = 37.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
x + 2.5 = 6.103277808

Simplifying
x + 2.5 = 6.103277808

Reorder the terms:
2.5 + x = 6.103277808

Solving
2.5 + x = 6.103277808

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 6.103277808 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.103277808 + -2.5
x = 6.103277808 + -2.5

Combine like terms: 6.103277808 + -2.5 = 3.603277808
x = 3.603277808

Simplifying
x = 3.603277808


Subproblem 2
x + 2.5 = -6.103277808

Simplifying
x + 2.5 = -6.103277808

Reorder the terms:
2.5 + x = -6.103277808

Solving
2.5 + x = -6.103277808

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -6.103277808 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.103277808 + -2.5
x = -6.103277808 + -2.5

Combine like terms: -6.103277808 + -2.5 = -8.603277808
x = -8.603277808

Simplifying
x = -8.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.603277808, -8.603277808}

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