-36t^2+162t+16=0

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Solution for -36t^2+162t+16=0 equation: 


Simplifying
-36t2 + 162t + 16 = 0

Reorder the terms:
16 + 162t + -36t2 = 0

Solving
16 + 162t + -36t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 81t + -18t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + 81t + -18t2)' equal to zero and attempt to solve:

Simplifying
8 + 81t + -18t2 = 0

Solving
8 + 81t + -18t2 = 0

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
-0.4444444444 + -4.5t + t2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -4.5t + 0.4444444444 + t2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -4.5t + t2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -4.5t + t2 = 0 + 0.4444444444
-4.5t + t2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-4.5t + t2 = 0.4444444444

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 = 0.4444444444 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = 0.4444444444 + 5.0625

Combine like terms: 0.4444444444 + 5.0625 = 5.5069444444
5.0625 + -4.5t + t2 = 5.5069444444

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = 5.5069444444

Calculate the square root of the right side: 2.346687973

Break this problem into two subproblems by setting 
(t + -2.25) equal to 2.346687973 and -2.346687973.


Subproblem 1
t + -2.25 = 2.346687973

Simplifying
t + -2.25 = 2.346687973

Reorder the terms:
-2.25 + t = 2.346687973

Solving
-2.25 + t = 2.346687973

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 = 2.346687973 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = 2.346687973 + 2.25
t = 2.346687973 + 2.25

Combine like terms: 2.346687973 + 2.25 = 4.596687973
t = 4.596687973

Simplifying
t = 4.596687973


Subproblem 2
t + -2.25 = -2.346687973

Simplifying
t + -2.25 = -2.346687973

Reorder the terms:
-2.25 + t = -2.346687973

Solving
-2.25 + t = -2.346687973

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 = -2.346687973 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = -2.346687973 + 2.25
t = -2.346687973 + 2.25

Combine like terms: -2.346687973 + 2.25 = -0.096687973
t = -0.096687973

Simplifying
t = -0.096687973


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.596687973, -0.096687973}
Solution
t = {4.596687973, -0.096687973}

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