-16t^2+24t+114=50

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Solution for -16t^2+24t+114=50 equation: 


Simplifying
-16t2 + 24t + 114 = 50

Reorder the terms:
114 + 24t + -16t2 = 50

Solving
114 + 24t + -16t2 = 50

Solving for variable 't'.

Reorder the terms:
114 + -50 + 24t + -16t2 = 50 + -50

Combine like terms: 114 + -50 = 64
64 + 24t + -16t2 = 50 + -50

Combine like terms: 50 + -50 = 0
64 + 24t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + 3t + -2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(8 + 3t + -2t2)' equal to zero and attempt to solve:

Simplifying
8 + 3t + -2t2 = 0

Solving
8 + 3t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4 + -1.5t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -1.5t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -1.5t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1.5t + t2 = 0 + 4
-1.5t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1.5t + t2 = 4

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = 4 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = 4 + 0.5625

Combine like terms: 4 + 0.5625 = 4.5625
0.5625 + -1.5t + t2 = 4.5625

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(t + -0.75) equal to 2.136000936 and -2.136000936.


Subproblem 1
t + -0.75 = 2.136000936

Simplifying
t + -0.75 = 2.136000936

Reorder the terms:
-0.75 + t = 2.136000936

Solving
-0.75 + t = 2.136000936

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 2.136000936 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 2.136000936 + 0.75
t = 2.136000936 + 0.75

Combine like terms: 2.136000936 + 0.75 = 2.886000936
t = 2.886000936

Simplifying
t = 2.886000936


Subproblem 2
t + -0.75 = -2.136000936

Simplifying
t + -0.75 = -2.136000936

Reorder the terms:
-0.75 + t = -2.136000936

Solving
-0.75 + t = -2.136000936

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -2.136000936 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -2.136000936 + 0.75
t = -2.136000936 + 0.75

Combine like terms: -2.136000936 + 0.75 = -1.386000936
t = -1.386000936

Simplifying
t = -1.386000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.886000936, -1.386000936}
Solution
t = {2.886000936, -1.386000936}

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