=(t^2+2t-5)

Solution for =(t^2+2t-5) equation:

Simplifying
0 = (t2 + 2t + -5)

Reorder the terms:
0 = (-5 + 2t + t2)

Remove parenthesis around (-5 + 2t + t2)
0 = -5 + 2t + t2

Solving
0 = -5 + 2t + t2

Solving for variable 't'.

Combine like terms: 0 + 5 = 5
5 + -2t + -1t2 = -5 + 2t + t2 + 5 + -2t + -1t2

Reorder the terms:
5 + -2t + -1t2 = -5 + 5 + 2t + -2t + t2 + -1t2

Combine like terms: -5 + 5 = 0
5 + -2t + -1t2 = 0 + 2t + -2t + t2 + -1t2
5 + -2t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
5 + -2t + -1t2 = 0 + t2 + -1t2
5 + -2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
5 + -2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 2t + t2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + 2t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2t + t2 = 0 + 5
2t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
2t + t2 = 5

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 5 + 1

Reorder the terms:
1 + 2t + t2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2t + t2 = 6

Factor a perfect square on the left side:
(t + 1)(t + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(t + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1
t + 1 = 2.449489743

Simplifying
t + 1 = 2.449489743

Reorder the terms:
1 + t = 2.449489743

Solving
1 + t = 2.449489743

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.449489743 + -1
t = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
t = 1.449489743

Simplifying
t = 1.449489743

Subproblem 2
t + 1 = -2.449489743

Simplifying
t + 1 = -2.449489743

Reorder the terms:
1 + t = -2.449489743

Solving
1 + t = -2.449489743

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.449489743 + -1
t = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
t = -3.449489743

Simplifying
t = -3.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.449489743, -3.449489743}