t^2+3t-31=0

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

Simplifying
t2 + 3t + -31 = 0

Reorder the terms:
-31 + 3t + t2 = 0

Solving
-31 + 3t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 3t + 31 + t2 = 0 + 31

Reorder the terms:
-31 + 31 + 3t + t2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 3t + t2 = 0 + 31
3t + t2 = 0 + 31

Combine like terms: 0 + 31 = 31
3t + t2 = 31

The t term is 3t.  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.
3t + 2.25 + t2 = 31 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 31 + 2.25

Combine like terms: 31 + 2.25 = 33.25
2.25 + 3t + t2 = 33.25

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

Calculate the square root of the right side: 5.766281297

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

Subproblem 1
t + 1.5 = 5.766281297

Simplifying
t + 1.5 = 5.766281297

Reorder the terms:
1.5 + t = 5.766281297

Solving
1.5 + t = 5.766281297

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 5.766281297 + -1.5

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

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

Simplifying
t = 4.266281297

Subproblem 2
t + 1.5 = -5.766281297

Simplifying
t + 1.5 = -5.766281297

Reorder the terms:
1.5 + t = -5.766281297

Solving
1.5 + t = -5.766281297

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -5.766281297 + -1.5

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

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

Simplifying
t = -7.266281297

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