14.7=19.6t-4.9t^2

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Solution for 14.7=19.6t-4.9t^2 equation:


Simplifying
14.7 = 19.6t + -4.9t2

Solving
14.7 = 19.6t + -4.9t2

Solving for variable 't'.

Reorder the terms:
14.7 + -19.6t + 4.9t2 = 19.6t + -19.6t + -4.9t2 + 4.9t2

Combine like terms: 19.6t + -19.6t = 0.0
14.7 + -19.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
14.7 + -19.6t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
14.7 + -19.6t + 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 + -4t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -4t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -4t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t + t2 = 0 + -3
-4t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4t + t2 = -3

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -3 + 4

Reorder the terms:
4 + -4t + t2 = -3 + 4

Combine like terms: -3 + 4 = 1
4 + -4t + t2 = 1

Factor a perfect square on the left side:
(t + -2)(t + -2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(t + -2) equal to 1 and -1.

Subproblem 1

t + -2 = 1 Simplifying t + -2 = 1 Reorder the terms: -2 + t = 1 Solving -2 + t = 1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1 + 2 t = 1 + 2 Combine like terms: 1 + 2 = 3 t = 3 Simplifying t = 3

Subproblem 2

t + -2 = -1 Simplifying t + -2 = -1 Reorder the terms: -2 + t = -1 Solving -2 + t = -1 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1 + 2 t = -1 + 2 Combine like terms: -1 + 2 = 1 t = 1 Simplifying t = 1

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3, 1}

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