-16t^2+110t+150=0

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Solution for -16t^2+110t+150=0 equation: 


Simplifying
-16t2 + 110t + 150 = 0

Reorder the terms:
150 + 110t + -16t2 = 0

Solving
150 + 110t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + 55t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + 55t + -8t2)' equal to zero and attempt to solve:

Simplifying
75 + 55t + -8t2 = 0

Solving
75 + 55t + -8t2 = 0

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

Divide each side by '-8'.
-9.375 + -6.875t + t2 = 0

Move the constant term to the right:

Add '9.375' to each side of the equation.
-9.375 + -6.875t + 9.375 + t2 = 0 + 9.375

Reorder the terms:
-9.375 + 9.375 + -6.875t + t2 = 0 + 9.375

Combine like terms: -9.375 + 9.375 = 0.000
0.000 + -6.875t + t2 = 0 + 9.375
-6.875t + t2 = 0 + 9.375

Combine like terms: 0 + 9.375 = 9.375
-6.875t + t2 = 9.375

The t term is -6.875t.  Take half its coefficient (-3.4375).
Square it (11.81640625) and add it to both sides.

Add '11.81640625' to each side of the equation.
-6.875t + 11.81640625 + t2 = 9.375 + 11.81640625

Reorder the terms:
11.81640625 + -6.875t + t2 = 9.375 + 11.81640625

Combine like terms: 9.375 + 11.81640625 = 21.19140625
11.81640625 + -6.875t + t2 = 21.19140625

Factor a perfect square on the left side:
(t + -3.4375)(t + -3.4375) = 21.19140625

Calculate the square root of the right side: 4.603412457

Break this problem into two subproblems by setting 
(t + -3.4375) equal to 4.603412457 and -4.603412457.


Subproblem 1
t + -3.4375 = 4.603412457

Simplifying
t + -3.4375 = 4.603412457

Reorder the terms:
-3.4375 + t = 4.603412457

Solving
-3.4375 + t = 4.603412457

Solving for variable 't'.

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

Add '3.4375' to each side of the equation.
-3.4375 + 3.4375 + t = 4.603412457 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = 4.603412457 + 3.4375
t = 4.603412457 + 3.4375

Combine like terms: 4.603412457 + 3.4375 = 8.040912457
t = 8.040912457

Simplifying
t = 8.040912457


Subproblem 2
t + -3.4375 = -4.603412457

Simplifying
t + -3.4375 = -4.603412457

Reorder the terms:
-3.4375 + t = -4.603412457

Solving
-3.4375 + t = -4.603412457

Solving for variable 't'.

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

Add '3.4375' to each side of the equation.
-3.4375 + 3.4375 + t = -4.603412457 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = -4.603412457 + 3.4375
t = -4.603412457 + 3.4375

Combine like terms: -4.603412457 + 3.4375 = -1.165912457
t = -1.165912457

Simplifying
t = -1.165912457


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.040912457, -1.165912457}
Solution
t = {8.040912457, -1.165912457}

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