15=30t+4.9t^2

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Solution for 15=30t+4.9t^2 equation:


Simplifying
15 = 30t + 4.9t2

Solving
15 = 30t + 4.9t2

Solving for variable 't'.

Reorder the terms:
15 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2

Combine like terms: 30t + -30t = 0
15 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2
15 + -30t + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
15 + -30t + -4.9t2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-3.06122449 + 6.12244898t + t2 = 0

Move the constant term to the right:

Add '3.06122449' to each side of the equation.
-3.06122449 + 6.12244898t + 3.06122449 + t2 = 0 + 3.06122449

Reorder the terms:
-3.06122449 + 3.06122449 + 6.12244898t + t2 = 0 + 3.06122449

Combine like terms: -3.06122449 + 3.06122449 = 0.00000000
0.00000000 + 6.12244898t + t2 = 0 + 3.06122449
6.12244898t + t2 = 0 + 3.06122449

Combine like terms: 0 + 3.06122449 = 3.06122449
6.12244898t + t2 = 3.06122449

The t term is 6.12244898t.  Take half its coefficient (3.06122449).
Square it (9.371095378) and add it to both sides.

Add '9.371095378' to each side of the equation.
6.12244898t + 9.371095378 + t2 = 3.06122449 + 9.371095378

Reorder the terms:
9.371095378 + 6.12244898t + t2 = 3.06122449 + 9.371095378

Combine like terms: 3.06122449 + 9.371095378 = 12.432319868
9.371095378 + 6.12244898t + t2 = 12.432319868

Factor a perfect square on the left side:
(t + 3.06122449)(t + 3.06122449) = 12.432319868

Calculate the square root of the right side: 3.525949499

Break this problem into two subproblems by setting 
(t + 3.06122449) equal to 3.525949499 and -3.525949499.

Subproblem 1

t + 3.06122449 = 3.525949499 Simplifying t + 3.06122449 = 3.525949499 Reorder the terms: 3.06122449 + t = 3.525949499 Solving 3.06122449 + t = 3.525949499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = 3.525949499 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 3.525949499 + -3.06122449 t = 3.525949499 + -3.06122449 Combine like terms: 3.525949499 + -3.06122449 = 0.464725009 t = 0.464725009 Simplifying t = 0.464725009

Subproblem 2

t + 3.06122449 = -3.525949499 Simplifying t + 3.06122449 = -3.525949499 Reorder the terms: 3.06122449 + t = -3.525949499 Solving 3.06122449 + t = -3.525949499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = -3.525949499 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -3.525949499 + -3.06122449 t = -3.525949499 + -3.06122449 Combine like terms: -3.525949499 + -3.06122449 = -6.587173989 t = -6.587173989 Simplifying t = -6.587173989

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.464725009, -6.587173989}

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