5t^2-14t-98=0

Solution for 5t^2-14t-98=0 equation:

Simplifying
5t2 + -14t + -98 = 0

Reorder the terms:
-98 + -14t + 5t2 = 0

Solving
-98 + -14t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
-19.6 + -2.8t + t2 = 0

Move the constant term to the right:

Add '19.6' to each side of the equation.
-19.6 + -2.8t + 19.6 + t2 = 0 + 19.6

Reorder the terms:
-19.6 + 19.6 + -2.8t + t2 = 0 + 19.6

Combine like terms: -19.6 + 19.6 = 0.0
0.0 + -2.8t + t2 = 0 + 19.6
-2.8t + t2 = 0 + 19.6

Combine like terms: 0 + 19.6 = 19.6
-2.8t + t2 = 19.6

The t term is -2.8t.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8t + 1.96 + t2 = 19.6 + 1.96

Reorder the terms:
1.96 + -2.8t + t2 = 19.6 + 1.96

Combine like terms: 19.6 + 1.96 = 21.56
1.96 + -2.8t + t2 = 21.56

Factor a perfect square on the left side:
(t + -1.4)(t + -1.4) = 21.56

Calculate the square root of the right side: 4.643274706

Break this problem into two subproblems by setting 
(t + -1.4) equal to 4.643274706 and -4.643274706.

Subproblem 1
t + -1.4 = 4.643274706

Simplifying
t + -1.4 = 4.643274706

Reorder the terms:
-1.4 + t = 4.643274706

Solving
-1.4 + t = 4.643274706

Solving for variable 't'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + t = 4.643274706 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + t = 4.643274706 + 1.4
t = 4.643274706 + 1.4

Combine like terms: 4.643274706 + 1.4 = 6.043274706
t = 6.043274706

Simplifying
t = 6.043274706

Subproblem 2
t + -1.4 = -4.643274706

Simplifying
t + -1.4 = -4.643274706

Reorder the terms:
-1.4 + t = -4.643274706

Solving
-1.4 + t = -4.643274706

Solving for variable 't'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + t = -4.643274706 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + t = -4.643274706 + 1.4
t = -4.643274706 + 1.4

Combine like terms: -4.643274706 + 1.4 = -3.243274706
t = -3.243274706

Simplifying
t = -3.243274706

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.043274706, -3.243274706}