t^2+8t-36=0

Solution for t^2+8t-36=0 equation:

Simplifying
t2 + 8t + -36 = 0

Reorder the terms:
-36 + 8t + t2 = 0

Solving
-36 + 8t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 8t + 36 + t2 = 0 + 36

Reorder the terms:
-36 + 36 + 8t + t2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 8t + t2 = 0 + 36
8t + t2 = 0 + 36

Combine like terms: 0 + 36 = 36
8t + t2 = 36

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 36 + 16

Reorder the terms:
16 + 8t + t2 = 36 + 16

Combine like terms: 36 + 16 = 52
16 + 8t + t2 = 52

Factor a perfect square on the left side:
(t + 4)(t + 4) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(t + 4) equal to 7.211102551 and -7.211102551.

Subproblem 1
t + 4 = 7.211102551

Simplifying
t + 4 = 7.211102551

Reorder the terms:
4 + t = 7.211102551

Solving
4 + t = 7.211102551

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + t = 7.211102551 + -4
t = 7.211102551 + -4

Combine like terms: 7.211102551 + -4 = 3.211102551
t = 3.211102551

Simplifying
t = 3.211102551

Subproblem 2
t + 4 = -7.211102551

Simplifying
t + 4 = -7.211102551

Reorder the terms:
4 + t = -7.211102551

Solving
4 + t = -7.211102551

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -7.211102551 + -4

Combine like terms: 4 + -4 = 0
0 + t = -7.211102551 + -4
t = -7.211102551 + -4

Combine like terms: -7.211102551 + -4 = -11.211102551
t = -11.211102551

Simplifying
t = -11.211102551

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.211102551, -11.211102551}