-4.9t^2+28.7t+4.2=0

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Solution for -4.9t^2+28.7t+4.2=0 equation: 


Simplifying
-4.9t2 + 28.7t + 4.2 = 0

Reorder the terms:
4.2 + 28.7t + -4.9t2 = 0

Solving
4.2 + 28.7t + -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'.
-0.8571428571 + -5.857142857t + t2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -5.857142857t + 0.8571428571 + t2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -5.857142857t + t2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -5.857142857t + t2 = 0 + 0.8571428571
-5.857142857t + t2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-5.857142857t + t2 = 0.8571428571

The t term is -5.857142857t.  Take half its coefficient (-2.928571429).
Square it (8.576530615) and add it to both sides.

Add '8.576530615' to each side of the equation.
-5.857142857t + 8.576530615 + t2 = 0.8571428571 + 8.576530615

Reorder the terms:
8.576530615 + -5.857142857t + t2 = 0.8571428571 + 8.576530615

Combine like terms: 0.8571428571 + 8.576530615 = 9.4336734721
8.576530615 + -5.857142857t + t2 = 9.4336734721

Factor a perfect square on the left side:
(t + -2.928571429)(t + -2.928571429) = 9.4336734721

Calculate the square root of the right side: 3.071428572

Break this problem into two subproblems by setting 
(t + -2.928571429) equal to 3.071428572 and -3.071428572.


Subproblem 1
t + -2.928571429 = 3.071428572

Simplifying
t + -2.928571429 = 3.071428572

Reorder the terms:
-2.928571429 + t = 3.071428572

Solving
-2.928571429 + t = 3.071428572

Solving for variable 't'.

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

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + t = 3.071428572 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + t = 3.071428572 + 2.928571429
t = 3.071428572 + 2.928571429

Combine like terms: 3.071428572 + 2.928571429 = 6.000000001
t = 6.000000001

Simplifying
t = 6.000000001


Subproblem 2
t + -2.928571429 = -3.071428572

Simplifying
t + -2.928571429 = -3.071428572

Reorder the terms:
-2.928571429 + t = -3.071428572

Solving
-2.928571429 + t = -3.071428572

Solving for variable 't'.

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

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + t = -3.071428572 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + t = -3.071428572 + 2.928571429
t = -3.071428572 + 2.928571429

Combine like terms: -3.071428572 + 2.928571429 = -0.142857143
t = -0.142857143

Simplifying
t = -0.142857143


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.000000001, -0.142857143}

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