t^2+2t-19=0

Solution for t^2+2t-19=0 equation:

Simplifying
t2 + 2t + -19 = 0

Reorder the terms:
-19 + 2t + t2 = 0

Solving
-19 + 2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2t + 19 + t2 = 0 + 19

Reorder the terms:
-19 + 19 + 2t + t2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2t + t2 = 0 + 19
2t + t2 = 0 + 19

Combine like terms: 0 + 19 = 19
2t + t2 = 19

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 = 19 + 1

Reorder the terms:
1 + 2t + t2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + 2t + t2 = 20

Factor a perfect square on the left side:
(t + 1)(t + 1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(t + 1) equal to 4.472135955 and -4.472135955.

Subproblem 1
t + 1 = 4.472135955

Simplifying
t + 1 = 4.472135955

Reorder the terms:
1 + t = 4.472135955

Solving
1 + t = 4.472135955

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 = 4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4.472135955 + -1
t = 4.472135955 + -1

Combine like terms: 4.472135955 + -1 = 3.472135955
t = 3.472135955

Simplifying
t = 3.472135955

Subproblem 2
t + 1 = -4.472135955

Simplifying
t + 1 = -4.472135955

Reorder the terms:
1 + t = -4.472135955

Solving
1 + t = -4.472135955

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 = -4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4.472135955 + -1
t = -4.472135955 + -1

Combine like terms: -4.472135955 + -1 = -5.472135955
t = -5.472135955

Simplifying
t = -5.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.472135955, -5.472135955}