0=-4.9t^2+14.7t+12

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Solution for 0=-4.9t^2+14.7t+12 equation:


Simplifying
0 = -4.9t2 + 14.7t + 12

Reorder the terms:
0 = 12 + 14.7t + -4.9t2

Solving
0 = 12 + 14.7t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -12 = -12
-12 + -14.7t + 4.9t2 = 12 + 14.7t + -4.9t2 + -12 + -14.7t + 4.9t2

Reorder the terms:
-12 + -14.7t + 4.9t2 = 12 + -12 + 14.7t + -14.7t + -4.9t2 + 4.9t2

Combine like terms: 12 + -12 = 0
-12 + -14.7t + 4.9t2 = 0 + 14.7t + -14.7t + -4.9t2 + 4.9t2
-12 + -14.7t + 4.9t2 = 14.7t + -14.7t + -4.9t2 + 4.9t2

Combine like terms: 14.7t + -14.7t = 0.0
-12 + -14.7t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-12 + -14.7t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-12 + -14.7t + 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'.
-2.448979592 + -3t + t2 = 0

Move the constant term to the right:

Add '2.448979592' to each side of the equation.
-2.448979592 + -3t + 2.448979592 + t2 = 0 + 2.448979592

Reorder the terms:
-2.448979592 + 2.448979592 + -3t + t2 = 0 + 2.448979592

Combine like terms: -2.448979592 + 2.448979592 = 0.000000000
0.000000000 + -3t + t2 = 0 + 2.448979592
-3t + t2 = 0 + 2.448979592

Combine like terms: 0 + 2.448979592 = 2.448979592
-3t + t2 = 2.448979592

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 2.448979592 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 2.448979592 + 2.25

Combine like terms: 2.448979592 + 2.25 = 4.698979592
2.25 + -3t + t2 = 4.698979592

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 4.698979592

Calculate the square root of the right side: 2.167712987

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.167712987 and -2.167712987.

Subproblem 1

t + -1.5 = 2.167712987 Simplifying t + -1.5 = 2.167712987 Reorder the terms: -1.5 + t = 2.167712987 Solving -1.5 + t = 2.167712987 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 2.167712987 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 2.167712987 + 1.5 t = 2.167712987 + 1.5 Combine like terms: 2.167712987 + 1.5 = 3.667712987 t = 3.667712987 Simplifying t = 3.667712987

Subproblem 2

t + -1.5 = -2.167712987 Simplifying t + -1.5 = -2.167712987 Reorder the terms: -1.5 + t = -2.167712987 Solving -1.5 + t = -2.167712987 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -2.167712987 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -2.167712987 + 1.5 t = -2.167712987 + 1.5 Combine like terms: -2.167712987 + 1.5 = -0.667712987 t = -0.667712987 Simplifying t = -0.667712987

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.667712987, -0.667712987}

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