0=-0.05t^2+30t+6

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Solution for 0=-0.05t^2+30t+6 equation:


Simplifying
0 = -0.05t2 + 30t + 6

Reorder the terms:
0 = 6 + 30t + -0.05t2

Solving
0 = 6 + 30t + -0.05t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -30t + 0.05t2 = 6 + 30t + -0.05t2 + -6 + -30t + 0.05t2

Reorder the terms:
-6 + -30t + 0.05t2 = 6 + -6 + 30t + -30t + -0.05t2 + 0.05t2

Combine like terms: 6 + -6 = 0
-6 + -30t + 0.05t2 = 0 + 30t + -30t + -0.05t2 + 0.05t2
-6 + -30t + 0.05t2 = 30t + -30t + -0.05t2 + 0.05t2

Combine like terms: 30t + -30t = 0
-6 + -30t + 0.05t2 = 0 + -0.05t2 + 0.05t2
-6 + -30t + 0.05t2 = -0.05t2 + 0.05t2

Combine like terms: -0.05t2 + 0.05t2 = 0.00
-6 + -30t + 0.05t2 = 0.00

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

Divide each side by '0.05'.
-120 + -600t + t2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -600t + 120 + t2 = 0 + 120

Reorder the terms:
-120 + 120 + -600t + t2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -600t + t2 = 0 + 120
-600t + t2 = 0 + 120

Combine like terms: 0 + 120 = 120
-600t + t2 = 120

The t term is -600t.  Take half its coefficient (-300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
-600t + 90000 + t2 = 120 + 90000

Reorder the terms:
90000 + -600t + t2 = 120 + 90000

Combine like terms: 120 + 90000 = 90120
90000 + -600t + t2 = 90120

Factor a perfect square on the left side:
(t + -300)(t + -300) = 90120

Calculate the square root of the right side: 300.199933378

Break this problem into two subproblems by setting 
(t + -300) equal to 300.199933378 and -300.199933378.

Subproblem 1

t + -300 = 300.199933378 Simplifying t + -300 = 300.199933378 Reorder the terms: -300 + t = 300.199933378 Solving -300 + t = 300.199933378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + t = 300.199933378 + 300 Combine like terms: -300 + 300 = 0 0 + t = 300.199933378 + 300 t = 300.199933378 + 300 Combine like terms: 300.199933378 + 300 = 600.199933378 t = 600.199933378 Simplifying t = 600.199933378

Subproblem 2

t + -300 = -300.199933378 Simplifying t + -300 = -300.199933378 Reorder the terms: -300 + t = -300.199933378 Solving -300 + t = -300.199933378 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + t = -300.199933378 + 300 Combine like terms: -300 + 300 = 0 0 + t = -300.199933378 + 300 t = -300.199933378 + 300 Combine like terms: -300.199933378 + 300 = -0.199933378 t = -0.199933378 Simplifying t = -0.199933378

Solution

The solution to the problem is based on the solutions from the subproblems. t = {600.199933378, -0.199933378}

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