t^2+6t-34=0

Solution for t^2+6t-34=0 equation:

Simplifying
t2 + 6t + -34 = 0

Reorder the terms:
-34 + 6t + t2 = 0

Solving
-34 + 6t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 6t + 34 + t2 = 0 + 34

Reorder the terms:
-34 + 34 + 6t + t2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 6t + t2 = 0 + 34
6t + t2 = 0 + 34

Combine like terms: 0 + 34 = 34
6t + t2 = 34

The t term is 6t.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6t + 9 + t2 = 34 + 9

Reorder the terms:
9 + 6t + t2 = 34 + 9

Combine like terms: 34 + 9 = 43
9 + 6t + t2 = 43

Factor a perfect square on the left side:
(t + 3)(t + 3) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(t + 3) equal to 6.557438524 and -6.557438524.

Subproblem 1
t + 3 = 6.557438524

Simplifying
t + 3 = 6.557438524

Reorder the terms:
3 + t = 6.557438524

Solving
3 + t = 6.557438524

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = 6.557438524 + -3

Combine like terms: 3 + -3 = 0
0 + t = 6.557438524 + -3
t = 6.557438524 + -3

Combine like terms: 6.557438524 + -3 = 3.557438524
t = 3.557438524

Simplifying
t = 3.557438524

Subproblem 2
t + 3 = -6.557438524

Simplifying
t + 3 = -6.557438524

Reorder the terms:
3 + t = -6.557438524

Solving
3 + t = -6.557438524

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = -6.557438524 + -3

Combine like terms: 3 + -3 = 0
0 + t = -6.557438524 + -3
t = -6.557438524 + -3

Combine like terms: -6.557438524 + -3 = -9.557438524
t = -9.557438524

Simplifying
t = -9.557438524

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.557438524, -9.557438524}