t^2+2t-30=0

Solution for t^2+2t-30=0 equation:

Simplifying
t2 + 2t + -30 = 0

Reorder the terms:
-30 + 2t + t2 = 0

Solving
-30 + 2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2t + 30 + t2 = 0 + 30

Reorder the terms:
-30 + 30 + 2t + t2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2t + t2 = 0 + 30
2t + t2 = 0 + 30

Combine like terms: 0 + 30 = 30
2t + t2 = 30

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 = 30 + 1

Reorder the terms:
1 + 2t + t2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2t + t2 = 31

Factor a perfect square on the left side:
(t + 1)(t + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(t + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
t + 1 = 5.567764363

Simplifying
t + 1 = 5.567764363

Reorder the terms:
1 + t = 5.567764363

Solving
1 + t = 5.567764363

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 = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + t = 5.567764363 + -1
t = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
t = 4.567764363

Simplifying
t = 4.567764363

Subproblem 2
t + 1 = -5.567764363

Simplifying
t + 1 = -5.567764363

Reorder the terms:
1 + t = -5.567764363

Solving
1 + t = -5.567764363

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 = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + t = -5.567764363 + -1
t = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
t = -6.567764363

Simplifying
t = -6.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.567764363, -6.567764363}