16t^2+150t+50=0

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Solution for 16t^2+150t+50=0 equation: 


Simplifying
16t2 + 150t + 50 = 0

Reorder the terms:
50 + 150t + 16t2 = 0

Solving
50 + 150t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 75t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 75t + 8t2)' equal to zero and attempt to solve:

Simplifying
25 + 75t + 8t2 = 0

Solving
25 + 75t + 8t2 = 0

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

Divide each side by '8'.
3.125 + 9.375t + t2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + 9.375t + -3.125 + t2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + 9.375t + t2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + 9.375t + t2 = 0 + -3.125
9.375t + t2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
9.375t + t2 = -3.125

The t term is 9.375t.  Take half its coefficient (4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
9.375t + 21.97265625 + t2 = -3.125 + 21.97265625

Reorder the terms:
21.97265625 + 9.375t + t2 = -3.125 + 21.97265625

Combine like terms: -3.125 + 21.97265625 = 18.84765625
21.97265625 + 9.375t + t2 = 18.84765625

Factor a perfect square on the left side:
(t + 4.6875)(t + 4.6875) = 18.84765625

Calculate the square root of the right side: 4.341388747

Break this problem into two subproblems by setting 
(t + 4.6875) equal to 4.341388747 and -4.341388747.


Subproblem 1
t + 4.6875 = 4.341388747

Simplifying
t + 4.6875 = 4.341388747

Reorder the terms:
4.6875 + t = 4.341388747

Solving
4.6875 + t = 4.341388747

Solving for variable 't'.

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

Add '-4.6875' to each side of the equation.
4.6875 + -4.6875 + t = 4.341388747 + -4.6875

Combine like terms: 4.6875 + -4.6875 = 0.0000
0.0000 + t = 4.341388747 + -4.6875
t = 4.341388747 + -4.6875

Combine like terms: 4.341388747 + -4.6875 = -0.346111253
t = -0.346111253

Simplifying
t = -0.346111253


Subproblem 2
t + 4.6875 = -4.341388747

Simplifying
t + 4.6875 = -4.341388747

Reorder the terms:
4.6875 + t = -4.341388747

Solving
4.6875 + t = -4.341388747

Solving for variable 't'.

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

Add '-4.6875' to each side of the equation.
4.6875 + -4.6875 + t = -4.341388747 + -4.6875

Combine like terms: 4.6875 + -4.6875 = 0.0000
0.0000 + t = -4.341388747 + -4.6875
t = -4.341388747 + -4.6875

Combine like terms: -4.341388747 + -4.6875 = -9.028888747
t = -9.028888747

Simplifying
t = -9.028888747


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.346111253, -9.028888747}
Solution
t = {-0.346111253, -9.028888747}

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