t^2+2t-38=0

Solution for t^2+2t-38=0 equation:

Simplifying
t2 + 2t + -38 = 0

Reorder the terms:
-38 + 2t + t2 = 0

Solving
-38 + 2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 2t + 38 + t2 = 0 + 38

Reorder the terms:
-38 + 38 + 2t + t2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 2t + t2 = 0 + 38
2t + t2 = 0 + 38

Combine like terms: 0 + 38 = 38
2t + t2 = 38

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 = 38 + 1

Reorder the terms:
1 + 2t + t2 = 38 + 1

Combine like terms: 38 + 1 = 39
1 + 2t + t2 = 39

Factor a perfect square on the left side:
(t + 1)(t + 1) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(t + 1) equal to 6.244997998 and -6.244997998.

Subproblem 1
t + 1 = 6.244997998

Simplifying
t + 1 = 6.244997998

Reorder the terms:
1 + t = 6.244997998

Solving
1 + t = 6.244997998

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 = 6.244997998 + -1

Combine like terms: 1 + -1 = 0
0 + t = 6.244997998 + -1
t = 6.244997998 + -1

Combine like terms: 6.244997998 + -1 = 5.244997998
t = 5.244997998

Simplifying
t = 5.244997998

Subproblem 2
t + 1 = -6.244997998

Simplifying
t + 1 = -6.244997998

Reorder the terms:
1 + t = -6.244997998

Solving
1 + t = -6.244997998

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 = -6.244997998 + -1

Combine like terms: 1 + -1 = 0
0 + t = -6.244997998 + -1
t = -6.244997998 + -1

Combine like terms: -6.244997998 + -1 = -7.244997998
t = -7.244997998

Simplifying
t = -7.244997998

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.244997998, -7.244997998}