4t^2-19t-2=0

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Solution for 4t^2-19t-2=0 equation: 


Simplifying
4t2 + -19t + -2 = 0

Reorder the terms:
-2 + -19t + 4t2 = 0

Solving
-2 + -19t + 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'.
-0.5 + -4.75t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -4.75t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -4.75t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -4.75t + t2 = 0 + 0.5
-4.75t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-4.75t + t2 = 0.5

The t term is -4.75t.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75t + 5.640625 + t2 = 0.5 + 5.640625

Reorder the terms:
5.640625 + -4.75t + t2 = 0.5 + 5.640625

Combine like terms: 0.5 + 5.640625 = 6.140625
5.640625 + -4.75t + t2 = 6.140625

Factor a perfect square on the left side:
(t + -2.375)(t + -2.375) = 6.140625

Calculate the square root of the right side: 2.47802845

Break this problem into two subproblems by setting 
(t + -2.375) equal to 2.47802845 and -2.47802845.


Subproblem 1
t + -2.375 = 2.47802845

Simplifying
t + -2.375 = 2.47802845

Reorder the terms:
-2.375 + t = 2.47802845

Solving
-2.375 + t = 2.47802845

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = 2.47802845 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = 2.47802845 + 2.375
t = 2.47802845 + 2.375

Combine like terms: 2.47802845 + 2.375 = 4.85302845
t = 4.85302845

Simplifying
t = 4.85302845


Subproblem 2
t + -2.375 = -2.47802845

Simplifying
t + -2.375 = -2.47802845

Reorder the terms:
-2.375 + t = -2.47802845

Solving
-2.375 + t = -2.47802845

Solving for variable 't'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + t = -2.47802845 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + t = -2.47802845 + 2.375
t = -2.47802845 + 2.375

Combine like terms: -2.47802845 + 2.375 = -0.10302845
t = -0.10302845

Simplifying
t = -0.10302845


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.85302845, -0.10302845}

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