4t^2-11t-8=0

Solution for 4t^2-11t-8=0 equation:

Simplifying
4t2 + -11t + -8 = 0

Reorder the terms:
-8 + -11t + 4t2 = 0

Solving
-8 + -11t + 4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2 + -2.75t + t2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.75t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.75t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.75t + t2 = 0 + 2
-2.75t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.75t + t2 = 2

The t term is -2.75t.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75t + 1.890625 + t2 = 2 + 1.890625

Reorder the terms:
1.890625 + -2.75t + t2 = 2 + 1.890625

Combine like terms: 2 + 1.890625 = 3.890625
1.890625 + -2.75t + t2 = 3.890625

Factor a perfect square on the left side:
(t + -1.375)(t + -1.375) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(t + -1.375) equal to 1.97246673 and -1.97246673.

Subproblem 1
t + -1.375 = 1.97246673

Simplifying
t + -1.375 = 1.97246673

Reorder the terms:
-1.375 + t = 1.97246673

Solving
-1.375 + t = 1.97246673

Solving for variable 't'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + t = 1.97246673 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + t = 1.97246673 + 1.375
t = 1.97246673 + 1.375

Combine like terms: 1.97246673 + 1.375 = 3.34746673
t = 3.34746673

Simplifying
t = 3.34746673

Subproblem 2
t + -1.375 = -1.97246673

Simplifying
t + -1.375 = -1.97246673

Reorder the terms:
-1.375 + t = -1.97246673

Solving
-1.375 + t = -1.97246673

Solving for variable 't'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + t = -1.97246673 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + t = -1.97246673 + 1.375
t = -1.97246673 + 1.375

Combine like terms: -1.97246673 + 1.375 = -0.59746673
t = -0.59746673

Simplifying
t = -0.59746673

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.34746673, -0.59746673}