0=3+30t-5t^2

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Solution for 0=3+30t-5t^2 equation:


Simplifying
0 = 3 + 30t + -5t2

Solving
0 = 3 + 30t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -30t + 5t2 = 3 + 30t + -5t2 + -3 + -30t + 5t2

Reorder the terms:
-3 + -30t + 5t2 = 3 + -3 + 30t + -30t + -5t2 + 5t2

Combine like terms: 3 + -3 = 0
-3 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2
-3 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
-3 + -30t + 5t2 = 0 + -5t2 + 5t2
-3 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-3 + -30t + 5t2 = 0

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

Divide each side by '5'.
-0.6 + -6t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -6t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -6t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -6t + t2 = 0 + 0.6
-6t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-6t + t2 = 0.6

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 0.6 + 9

Reorder the terms:
9 + -6t + t2 = 0.6 + 9

Combine like terms: 0.6 + 9 = 9.6
9 + -6t + t2 = 9.6

Factor a perfect square on the left side:
(t + -3)(t + -3) = 9.6

Calculate the square root of the right side: 3.098386677

Break this problem into two subproblems by setting 
(t + -3) equal to 3.098386677 and -3.098386677.

Subproblem 1

t + -3 = 3.098386677 Simplifying t + -3 = 3.098386677 Reorder the terms: -3 + t = 3.098386677 Solving -3 + t = 3.098386677 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.098386677 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.098386677 + 3 t = 3.098386677 + 3 Combine like terms: 3.098386677 + 3 = 6.098386677 t = 6.098386677 Simplifying t = 6.098386677

Subproblem 2

t + -3 = -3.098386677 Simplifying t + -3 = -3.098386677 Reorder the terms: -3 + t = -3.098386677 Solving -3 + t = -3.098386677 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.098386677 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.098386677 + 3 t = -3.098386677 + 3 Combine like terms: -3.098386677 + 3 = -0.098386677 t = -0.098386677 Simplifying t = -0.098386677

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.098386677, -0.098386677}

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