t^2+t-28=0

Solution for t^2+t-28=0 equation:

Simplifying
t2 + t + -28 = 0

Reorder the terms:
-28 + t + t2 = 0

Solving
-28 + t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + t + 28 + t2 = 0 + 28

Reorder the terms:
-28 + 28 + t + t2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + t + t2 = 0 + 28
t + t2 = 0 + 28

Combine like terms: 0 + 28 = 28
t + t2 = 28

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 = 28 + 0.25

Reorder the terms:
0.25 + t + t2 = 28 + 0.25

Combine like terms: 28 + 0.25 = 28.25
0.25 + t + t2 = 28.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(t + 0.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
t + 0.5 = 5.315072906

Simplifying
t + 0.5 = 5.315072906

Reorder the terms:
0.5 + t = 5.315072906

Solving
0.5 + t = 5.315072906

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 = 5.315072906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 5.315072906 + -0.5
t = 5.315072906 + -0.5

Combine like terms: 5.315072906 + -0.5 = 4.815072906
t = 4.815072906

Simplifying
t = 4.815072906

Subproblem 2
t + 0.5 = -5.315072906

Simplifying
t + 0.5 = -5.315072906

Reorder the terms:
0.5 + t = -5.315072906

Solving
0.5 + t = -5.315072906

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 = -5.315072906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -5.315072906 + -0.5
t = -5.315072906 + -0.5

Combine like terms: -5.315072906 + -0.5 = -5.815072906
t = -5.815072906

Simplifying
t = -5.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.815072906, -5.815072906}