-11=30t-5t^2

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Solution for -11=30t-5t^2 equation:


Simplifying
-11 = 30t + -5t2

Solving
-11 = 30t + -5t2

Solving for variable 't'.

Reorder the terms:
-11 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
-11 + -30t + 5t2 = 0 + -5t2 + 5t2
-11 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-11 + -30t + 5t2 = 0

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

Divide each side by '5'.
-2.2 + -6t + t2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -6t + 2.2 + t2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -6t + t2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -6t + t2 = 0 + 2.2
-6t + t2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-6t + t2 = 2.2

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 = 2.2 + 9

Reorder the terms:
9 + -6t + t2 = 2.2 + 9

Combine like terms: 2.2 + 9 = 11.2
9 + -6t + t2 = 11.2

Factor a perfect square on the left side:
(t + -3)(t + -3) = 11.2

Calculate the square root of the right side: 3.346640106

Break this problem into two subproblems by setting 
(t + -3) equal to 3.346640106 and -3.346640106.

Subproblem 1

t + -3 = 3.346640106 Simplifying t + -3 = 3.346640106 Reorder the terms: -3 + t = 3.346640106 Solving -3 + t = 3.346640106 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 = 3.346640106 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.346640106 + 3 t = 3.346640106 + 3 Combine like terms: 3.346640106 + 3 = 6.346640106 t = 6.346640106 Simplifying t = 6.346640106

Subproblem 2

t + -3 = -3.346640106 Simplifying t + -3 = -3.346640106 Reorder the terms: -3 + t = -3.346640106 Solving -3 + t = -3.346640106 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 = -3.346640106 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.346640106 + 3 t = -3.346640106 + 3 Combine like terms: -3.346640106 + 3 = -0.346640106 t = -0.346640106 Simplifying t = -0.346640106

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.346640106, -0.346640106}

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