10x^2-31x=-5

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

Simplifying
10x2 + -31x = -5

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

Solving
-31x + 10x2 = -5

Solving for variable 'x'.

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

Combine like terms: -5 + 5 = 0
5 + -31x + 10x2 = 0

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

Divide each side by '10'.
0.5 + -3.1x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3.1x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3.1x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3.1x + x2 = 0 + -0.5
-3.1x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3.1x + x2 = -0.5

The x term is -3.1x.  Take half its coefficient (-1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
-3.1x + 2.4025 + x2 = -0.5 + 2.4025

Reorder the terms:
2.4025 + -3.1x + x2 = -0.5 + 2.4025

Combine like terms: -0.5 + 2.4025 = 1.9025
2.4025 + -3.1x + x2 = 1.9025

Factor a perfect square on the left side:
(x + -1.55)(x + -1.55) = 1.9025

Calculate the square root of the right side: 1.379311422

Break this problem into two subproblems by setting 
(x + -1.55) equal to 1.379311422 and -1.379311422.

Subproblem 1
x + -1.55 = 1.379311422

Simplifying
x + -1.55 = 1.379311422

Reorder the terms:
-1.55 + x = 1.379311422

Solving
-1.55 + x = 1.379311422

Solving for variable 'x'.

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

Add '1.55' to each side of the equation.
-1.55 + 1.55 + x = 1.379311422 + 1.55

Combine like terms: -1.55 + 1.55 = 0.00
0.00 + x = 1.379311422 + 1.55
x = 1.379311422 + 1.55

Combine like terms: 1.379311422 + 1.55 = 2.929311422
x = 2.929311422

Simplifying
x = 2.929311422

Subproblem 2
x + -1.55 = -1.379311422

Simplifying
x + -1.55 = -1.379311422

Reorder the terms:
-1.55 + x = -1.379311422

Solving
-1.55 + x = -1.379311422

Solving for variable 'x'.

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

Add '1.55' to each side of the equation.
-1.55 + 1.55 + x = -1.379311422 + 1.55

Combine like terms: -1.55 + 1.55 = 0.00
0.00 + x = -1.379311422 + 1.55
x = -1.379311422 + 1.55

Combine like terms: -1.379311422 + 1.55 = 0.170688578
x = 0.170688578

Simplifying
x = 0.170688578

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.929311422, 0.170688578}