t^2-8t-3=0

Solution for t^2-8t-3=0 equation:

Simplifying
t2 + -8t + -3 = 0

Reorder the terms:
-3 + -8t + t2 = 0

Solving
-3 + -8t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + -8t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8t + t2 = 0 + 3
-8t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8t + t2 = 3

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 = 3 + 16

Reorder the terms:
16 + -8t + t2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8t + t2 = 19

Factor a perfect square on the left side:
(t + -4)(t + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(t + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1
t + -4 = 4.358898944

Simplifying
t + -4 = 4.358898944

Reorder the terms:
-4 + t = 4.358898944

Solving
-4 + t = 4.358898944

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 = 4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + t = 4.358898944 + 4
t = 4.358898944 + 4

Combine like terms: 4.358898944 + 4 = 8.358898944
t = 8.358898944

Simplifying
t = 8.358898944

Subproblem 2
t + -4 = -4.358898944

Simplifying
t + -4 = -4.358898944

Reorder the terms:
-4 + t = -4.358898944

Solving
-4 + t = -4.358898944

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 = -4.358898944 + 4

Combine like terms: -4 + 4 = 0
0 + t = -4.358898944 + 4
t = -4.358898944 + 4

Combine like terms: -4.358898944 + 4 = -0.358898944
t = -0.358898944

Simplifying
t = -0.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.358898944, -0.358898944}