16t^2-56t-62=0

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Solution for 16t^2-56t-62=0 equation: 


Simplifying
16t2 + -56t + -62 = 0

Reorder the terms:
-62 + -56t + 16t2 = 0

Solving
-62 + -56t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -28t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + -28t + 8t2)' equal to zero and attempt to solve:

Simplifying
-31 + -28t + 8t2 = 0

Solving
-31 + -28t + 8t2 = 0

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

Divide each side by '8'.
-3.875 + -3.5t + t2 = 0

Move the constant term to the right:

Add '3.875' to each side of the equation.
-3.875 + -3.5t + 3.875 + t2 = 0 + 3.875

Reorder the terms:
-3.875 + 3.875 + -3.5t + t2 = 0 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + -3.5t + t2 = 0 + 3.875
-3.5t + t2 = 0 + 3.875

Combine like terms: 0 + 3.875 = 3.875
-3.5t + t2 = 3.875

The t term is -3.5t.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5t + 3.0625 + t2 = 3.875 + 3.0625

Reorder the terms:
3.0625 + -3.5t + t2 = 3.875 + 3.0625

Combine like terms: 3.875 + 3.0625 = 6.9375
3.0625 + -3.5t + t2 = 6.9375

Factor a perfect square on the left side:
(t + -1.75)(t + -1.75) = 6.9375

Calculate the square root of the right side: 2.633913438

Break this problem into two subproblems by setting 
(t + -1.75) equal to 2.633913438 and -2.633913438.


Subproblem 1
t + -1.75 = 2.633913438

Simplifying
t + -1.75 = 2.633913438

Reorder the terms:
-1.75 + t = 2.633913438

Solving
-1.75 + t = 2.633913438

Solving for variable 't'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + t = 2.633913438 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + t = 2.633913438 + 1.75
t = 2.633913438 + 1.75

Combine like terms: 2.633913438 + 1.75 = 4.383913438
t = 4.383913438

Simplifying
t = 4.383913438


Subproblem 2
t + -1.75 = -2.633913438

Simplifying
t + -1.75 = -2.633913438

Reorder the terms:
-1.75 + t = -2.633913438

Solving
-1.75 + t = -2.633913438

Solving for variable 't'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + t = -2.633913438 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + t = -2.633913438 + 1.75
t = -2.633913438 + 1.75

Combine like terms: -2.633913438 + 1.75 = -0.883913438
t = -0.883913438

Simplifying
t = -0.883913438


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.383913438, -0.883913438}
Solution
t = {4.383913438, -0.883913438}

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