t^2+t-15=0

Solution for t^2+t-15=0 equation:

Simplifying
t2 + t + -15 = 0

Reorder the terms:
-15 + t + t2 = 0

Solving
-15 + t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + t + 15 + t2 = 0 + 15

Reorder the terms:
-15 + 15 + t + t2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + t + t2 = 0 + 15
t + t2 = 0 + 15

Combine like terms: 0 + 15 = 15
t + t2 = 15

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 15 + 0.25

Reorder the terms:
0.25 + t + t2 = 15 + 0.25

Combine like terms: 15 + 0.25 = 15.25
0.25 + t + t2 = 15.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(t + 0.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
t + 0.5 = 3.905124838

Simplifying
t + 0.5 = 3.905124838

Reorder the terms:
0.5 + t = 3.905124838

Solving
0.5 + t = 3.905124838

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 3.905124838 + -0.5
t = 3.905124838 + -0.5

Combine like terms: 3.905124838 + -0.5 = 3.405124838
t = 3.405124838

Simplifying
t = 3.405124838

Subproblem 2
t + 0.5 = -3.905124838

Simplifying
t + 0.5 = -3.905124838

Reorder the terms:
0.5 + t = -3.905124838

Solving
0.5 + t = -3.905124838

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -3.905124838 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -3.905124838 + -0.5
t = -3.905124838 + -0.5

Combine like terms: -3.905124838 + -0.5 = -4.405124838
t = -4.405124838

Simplifying
t = -4.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.405124838, -4.405124838}