-4.9t^2+38.5t+5.6=0

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Solution for -4.9t^2+38.5t+5.6=0 equation: 


Simplifying
-4.9t2 + 38.5t + 5.6 = 0

Reorder the terms:
5.6 + 38.5t + -4.9t2 = 0

Solving
5.6 + 38.5t + -4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '-4.9'.
-1.142857143 + -7.857142857t + t2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -7.857142857t + 1.142857143 + t2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -7.857142857t + t2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -7.857142857t + t2 = 0 + 1.142857143
-7.857142857t + t2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-7.857142857t + t2 = 1.142857143

The t term is -7.857142857t.  Take half its coefficient (-3.928571429).
Square it (15.43367347) and add it to both sides.

Add '15.43367347' to each side of the equation.
-7.857142857t + 15.43367347 + t2 = 1.142857143 + 15.43367347

Reorder the terms:
15.43367347 + -7.857142857t + t2 = 1.142857143 + 15.43367347

Combine like terms: 1.142857143 + 15.43367347 = 16.576530613
15.43367347 + -7.857142857t + t2 = 16.576530613

Factor a perfect square on the left side:
(t + -3.928571429)(t + -3.928571429) = 16.576530613

Calculate the square root of the right side: 4.071428572

Break this problem into two subproblems by setting 
(t + -3.928571429) equal to 4.071428572 and -4.071428572.


Subproblem 1
t + -3.928571429 = 4.071428572

Simplifying
t + -3.928571429 = 4.071428572

Reorder the terms:
-3.928571429 + t = 4.071428572

Solving
-3.928571429 + t = 4.071428572

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.928571429' to each side of the equation.
-3.928571429 + 3.928571429 + t = 4.071428572 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + t = 4.071428572 + 3.928571429
t = 4.071428572 + 3.928571429

Combine like terms: 4.071428572 + 3.928571429 = 8.000000001
t = 8.000000001

Simplifying
t = 8.000000001


Subproblem 2
t + -3.928571429 = -4.071428572

Simplifying
t + -3.928571429 = -4.071428572

Reorder the terms:
-3.928571429 + t = -4.071428572

Solving
-3.928571429 + t = -4.071428572

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.928571429' to each side of the equation.
-3.928571429 + 3.928571429 + t = -4.071428572 + 3.928571429

Combine like terms: -3.928571429 + 3.928571429 = 0.000000000
0.000000000 + t = -4.071428572 + 3.928571429
t = -4.071428572 + 3.928571429

Combine like terms: -4.071428572 + 3.928571429 = -0.142857143
t = -0.142857143

Simplifying
t = -0.142857143


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.000000001, -0.142857143}

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