4.9t^2-14t-94=0

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Solution for 4.9t^2-14t-94=0 equation: 


Simplifying
4.9t2 + -14t + -94 = 0

Reorder the terms:
-94 + -14t + 4.9t2 = 0

Solving
-94 + -14t + 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'.
-19.18367347 + -2.857142857t + t2 = 0

Move the constant term to the right:

Add '19.18367347' to each side of the equation.
-19.18367347 + -2.857142857t + 19.18367347 + t2 = 0 + 19.18367347

Reorder the terms:
-19.18367347 + 19.18367347 + -2.857142857t + t2 = 0 + 19.18367347

Combine like terms: -19.18367347 + 19.18367347 = 0.00000000
0.00000000 + -2.857142857t + t2 = 0 + 19.18367347
-2.857142857t + t2 = 0 + 19.18367347

Combine like terms: 0 + 19.18367347 = 19.18367347
-2.857142857t + t2 = 19.18367347

The t term is -2.857142857t.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857t + 2.040816328 + t2 = 19.18367347 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857t + t2 = 19.18367347 + 2.040816328

Combine like terms: 19.18367347 + 2.040816328 = 21.224489798
2.040816328 + -2.857142857t + t2 = 21.224489798

Factor a perfect square on the left side:
(t + -1.428571429)(t + -1.428571429) = 21.224489798

Calculate the square root of the right side: 4.607004428

Break this problem into two subproblems by setting 
(t + -1.428571429) equal to 4.607004428 and -4.607004428.


Subproblem 1
t + -1.428571429 = 4.607004428

Simplifying
t + -1.428571429 = 4.607004428

Reorder the terms:
-1.428571429 + t = 4.607004428

Solving
-1.428571429 + t = 4.607004428

Solving for variable 't'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + t = 4.607004428 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + t = 4.607004428 + 1.428571429
t = 4.607004428 + 1.428571429

Combine like terms: 4.607004428 + 1.428571429 = 6.035575857
t = 6.035575857

Simplifying
t = 6.035575857


Subproblem 2
t + -1.428571429 = -4.607004428

Simplifying
t + -1.428571429 = -4.607004428

Reorder the terms:
-1.428571429 + t = -4.607004428

Solving
-1.428571429 + t = -4.607004428

Solving for variable 't'.

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

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.428571429 + t = -4.607004428 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + t = -4.607004428 + 1.428571429
t = -4.607004428 + 1.428571429

Combine like terms: -4.607004428 + 1.428571429 = -3.178432999
t = -3.178432999

Simplifying
t = -3.178432999


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.035575857, -3.178432999}

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