t^2-18t-6=0

Solution for t^2-18t-6=0 equation:

Simplifying
t2 + -18t + -6 = 0

Reorder the terms:
-6 + -18t + t2 = 0

Solving
-6 + -18t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -18t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -18t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -18t + t2 = 0 + 6
-18t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-18t + t2 = 6

The t term is -18t.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18t + 81 + t2 = 6 + 81

Reorder the terms:
81 + -18t + t2 = 6 + 81

Combine like terms: 6 + 81 = 87
81 + -18t + t2 = 87

Factor a perfect square on the left side:
(t + -9)(t + -9) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(t + -9) equal to 9.327379053 and -9.327379053.

Subproblem 1
t + -9 = 9.327379053

Simplifying
t + -9 = 9.327379053

Reorder the terms:
-9 + t = 9.327379053

Solving
-9 + t = 9.327379053

Solving for variable 't'.

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

Add '9' to each side of the equation.
-9 + 9 + t = 9.327379053 + 9

Combine like terms: -9 + 9 = 0
0 + t = 9.327379053 + 9
t = 9.327379053 + 9

Combine like terms: 9.327379053 + 9 = 18.327379053
t = 18.327379053

Simplifying
t = 18.327379053

Subproblem 2
t + -9 = -9.327379053

Simplifying
t + -9 = -9.327379053

Reorder the terms:
-9 + t = -9.327379053

Solving
-9 + t = -9.327379053

Solving for variable 't'.

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

Add '9' to each side of the equation.
-9 + 9 + t = -9.327379053 + 9

Combine like terms: -9 + 9 = 0
0 + t = -9.327379053 + 9
t = -9.327379053 + 9

Combine like terms: -9.327379053 + 9 = -0.327379053
t = -0.327379053

Simplifying
t = -0.327379053

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.327379053, -0.327379053}