16t^2+72t+50=0

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Solution for 16t^2+72t+50=0 equation: 


Simplifying
16t2 + 72t + 50 = 0

Reorder the terms:
50 + 72t + 16t2 = 0

Solving
50 + 72t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 36t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 36t + 8t2)' equal to zero and attempt to solve:

Simplifying
25 + 36t + 8t2 = 0

Solving
25 + 36t + 8t2 = 0

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

Divide each side by '8'.
3.125 + 4.5t + t2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + 4.5t + -3.125 + t2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + 4.5t + t2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + 4.5t + t2 = 0 + -3.125
4.5t + t2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
4.5t + t2 = -3.125

The t term is 4.5t.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5t + 5.0625 + t2 = -3.125 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = -3.125 + 5.0625

Combine like terms: -3.125 + 5.0625 = 1.9375
5.0625 + 4.5t + t2 = 1.9375

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(t + 2.25) equal to 1.391941091 and -1.391941091.


Subproblem 1
t + 2.25 = 1.391941091

Simplifying
t + 2.25 = 1.391941091

Reorder the terms:
2.25 + t = 1.391941091

Solving
2.25 + t = 1.391941091

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = 1.391941091 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 1.391941091 + -2.25
t = 1.391941091 + -2.25

Combine like terms: 1.391941091 + -2.25 = -0.858058909
t = -0.858058909

Simplifying
t = -0.858058909


Subproblem 2
t + 2.25 = -1.391941091

Simplifying
t + 2.25 = -1.391941091

Reorder the terms:
2.25 + t = -1.391941091

Solving
2.25 + t = -1.391941091

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = -1.391941091 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -1.391941091 + -2.25
t = -1.391941091 + -2.25

Combine like terms: -1.391941091 + -2.25 = -3.641941091
t = -3.641941091

Simplifying
t = -3.641941091


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.858058909, -3.641941091}
Solution
t = {-0.858058909, -3.641941091}

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