t^2-6t-25=0

Solution for t^2-6t-25=0 equation:

Simplifying
t2 + -6t + -25 = 0

Reorder the terms:
-25 + -6t + t2 = 0

Solving
-25 + -6t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6t + 25 + t2 = 0 + 25

Reorder the terms:
-25 + 25 + -6t + t2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6t + t2 = 0 + 25
-6t + t2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6t + t2 = 25

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 = 25 + 9

Reorder the terms:
9 + -6t + t2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + -6t + t2 = 34

Factor a perfect square on the left side:
(t + -3)(t + -3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(t + -3) equal to 5.830951895 and -5.830951895.

Subproblem 1
t + -3 = 5.830951895

Simplifying
t + -3 = 5.830951895

Reorder the terms:
-3 + t = 5.830951895

Solving
-3 + t = 5.830951895

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 = 5.830951895 + 3

Combine like terms: -3 + 3 = 0
0 + t = 5.830951895 + 3
t = 5.830951895 + 3

Combine like terms: 5.830951895 + 3 = 8.830951895
t = 8.830951895

Simplifying
t = 8.830951895

Subproblem 2
t + -3 = -5.830951895

Simplifying
t + -3 = -5.830951895

Reorder the terms:
-3 + t = -5.830951895

Solving
-3 + t = -5.830951895

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 = -5.830951895 + 3

Combine like terms: -3 + 3 = 0
0 + t = -5.830951895 + 3
t = -5.830951895 + 3

Combine like terms: -5.830951895 + 3 = -2.830951895
t = -2.830951895

Simplifying
t = -2.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.830951895, -2.830951895}