16t^2-136t+220=0

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Solution for 16t^2-136t+220=0 equation: 


Simplifying
16t2 + -136t + 220 = 0

Reorder the terms:
220 + -136t + 16t2 = 0

Solving
220 + -136t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(55 + -34t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(55 + -34t + 4t2)' equal to zero and attempt to solve:

Simplifying
55 + -34t + 4t2 = 0

Solving
55 + -34t + 4t2 = 0

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

Divide each side by '4'.
13.75 + -8.5t + t2 = 0

Move the constant term to the right:

Add '-13.75' to each side of the equation.
13.75 + -8.5t + -13.75 + t2 = 0 + -13.75

Reorder the terms:
13.75 + -13.75 + -8.5t + t2 = 0 + -13.75

Combine like terms: 13.75 + -13.75 = 0.00
0.00 + -8.5t + t2 = 0 + -13.75
-8.5t + t2 = 0 + -13.75

Combine like terms: 0 + -13.75 = -13.75
-8.5t + t2 = -13.75

The t term is -8.5t.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5t + 18.0625 + t2 = -13.75 + 18.0625

Reorder the terms:
18.0625 + -8.5t + t2 = -13.75 + 18.0625

Combine like terms: -13.75 + 18.0625 = 4.3125
18.0625 + -8.5t + t2 = 4.3125

Factor a perfect square on the left side:
(t + -4.25)(t + -4.25) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(t + -4.25) equal to 2.076655966 and -2.076655966.


Subproblem 1
t + -4.25 = 2.076655966

Simplifying
t + -4.25 = 2.076655966

Reorder the terms:
-4.25 + t = 2.076655966

Solving
-4.25 + t = 2.076655966

Solving for variable 't'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + t = 2.076655966 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + t = 2.076655966 + 4.25
t = 2.076655966 + 4.25

Combine like terms: 2.076655966 + 4.25 = 6.326655966
t = 6.326655966

Simplifying
t = 6.326655966


Subproblem 2
t + -4.25 = -2.076655966

Simplifying
t + -4.25 = -2.076655966

Reorder the terms:
-4.25 + t = -2.076655966

Solving
-4.25 + t = -2.076655966

Solving for variable 't'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + t = -2.076655966 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + t = -2.076655966 + 4.25
t = -2.076655966 + 4.25

Combine like terms: -2.076655966 + 4.25 = 2.173344034
t = 2.173344034

Simplifying
t = 2.173344034


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.326655966, 2.173344034}
Solution
t = {6.326655966, 2.173344034}

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