0=-3t^2+36t-5

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Solution for 0=-3t^2+36t-5 equation:


Simplifying
0 = -3t2 + 36t + -5

Reorder the terms:
0 = -5 + 36t + -3t2

Solving
0 = -5 + 36t + -3t2

Solving for variable 't'.

Combine like terms: 0 + 5 = 5
5 + -36t + 3t2 = -5 + 36t + -3t2 + 5 + -36t + 3t2

Reorder the terms:
5 + -36t + 3t2 = -5 + 5 + 36t + -36t + -3t2 + 3t2

Combine like terms: -5 + 5 = 0
5 + -36t + 3t2 = 0 + 36t + -36t + -3t2 + 3t2
5 + -36t + 3t2 = 36t + -36t + -3t2 + 3t2

Combine like terms: 36t + -36t = 0
5 + -36t + 3t2 = 0 + -3t2 + 3t2
5 + -36t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
5 + -36t + 3t2 = 0

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

Divide each side by '3'.
1.666666667 + -12t + t2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -12t + -1.666666667 + t2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -12t + t2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -12t + t2 = 0 + -1.666666667
-12t + t2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-12t + t2 = -1.666666667

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -1.666666667 + 36

Reorder the terms:
36 + -12t + t2 = -1.666666667 + 36

Combine like terms: -1.666666667 + 36 = 34.333333333
36 + -12t + t2 = 34.333333333

Factor a perfect square on the left side:
(t + -6)(t + -6) = 34.333333333

Calculate the square root of the right side: 5.859465277

Break this problem into two subproblems by setting 
(t + -6) equal to 5.859465277 and -5.859465277.

Subproblem 1

t + -6 = 5.859465277 Simplifying t + -6 = 5.859465277 Reorder the terms: -6 + t = 5.859465277 Solving -6 + t = 5.859465277 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 5.859465277 + 6 Combine like terms: -6 + 6 = 0 0 + t = 5.859465277 + 6 t = 5.859465277 + 6 Combine like terms: 5.859465277 + 6 = 11.859465277 t = 11.859465277 Simplifying t = 11.859465277

Subproblem 2

t + -6 = -5.859465277 Simplifying t + -6 = -5.859465277 Reorder the terms: -6 + t = -5.859465277 Solving -6 + t = -5.859465277 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -5.859465277 + 6 Combine like terms: -6 + 6 = 0 0 + t = -5.859465277 + 6 t = -5.859465277 + 6 Combine like terms: -5.859465277 + 6 = 0.140534723 t = 0.140534723 Simplifying t = 0.140534723

Solution

The solution to the problem is based on the solutions from the subproblems. t = {11.859465277, 0.140534723}

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