-4.9t^2-11.2t+35=0

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Solution for -4.9t^2-11.2t+35=0 equation: 


Simplifying
-4.9t2 + -11.2t + 35 = 0

Reorder the terms:
35 + -11.2t + -4.9t2 = 0

Solving
35 + -11.2t + -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'.
-7.142857143 + 2.285714286t + t2 = 0

Move the constant term to the right:

Add '7.142857143' to each side of the equation.
-7.142857143 + 2.285714286t + 7.142857143 + t2 = 0 + 7.142857143

Reorder the terms:
-7.142857143 + 7.142857143 + 2.285714286t + t2 = 0 + 7.142857143

Combine like terms: -7.142857143 + 7.142857143 = 0.000000000
0.000000000 + 2.285714286t + t2 = 0 + 7.142857143
2.285714286t + t2 = 0 + 7.142857143

Combine like terms: 0 + 7.142857143 = 7.142857143
2.285714286t + t2 = 7.142857143

The t term is 2.285714286t.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286t + 1.306122449 + t2 = 7.142857143 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286t + t2 = 7.142857143 + 1.306122449

Combine like terms: 7.142857143 + 1.306122449 = 8.448979592
1.306122449 + 2.285714286t + t2 = 8.448979592

Factor a perfect square on the left side:
(t + 1.142857143)(t + 1.142857143) = 8.448979592

Calculate the square root of the right side: 2.90671285

Break this problem into two subproblems by setting 
(t + 1.142857143) equal to 2.90671285 and -2.90671285.


Subproblem 1
t + 1.142857143 = 2.90671285

Simplifying
t + 1.142857143 = 2.90671285

Reorder the terms:
1.142857143 + t = 2.90671285

Solving
1.142857143 + t = 2.90671285

Solving for variable 't'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + t = 2.90671285 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + t = 2.90671285 + -1.142857143
t = 2.90671285 + -1.142857143

Combine like terms: 2.90671285 + -1.142857143 = 1.763855707
t = 1.763855707

Simplifying
t = 1.763855707


Subproblem 2
t + 1.142857143 = -2.90671285

Simplifying
t + 1.142857143 = -2.90671285

Reorder the terms:
1.142857143 + t = -2.90671285

Solving
1.142857143 + t = -2.90671285

Solving for variable 't'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + t = -2.90671285 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + t = -2.90671285 + -1.142857143
t = -2.90671285 + -1.142857143

Combine like terms: -2.90671285 + -1.142857143 = -4.049569993
t = -4.049569993

Simplifying
t = -4.049569993


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.763855707, -4.049569993}

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