4.9*t^2+11*t-70=0

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Solution for 4.9*t^2+11*t-70=0 equation: 


Simplifying
4.9t2 + 11t + -70 = 0

Reorder the terms:
-70 + 11t + 4.9t2 = 0

Solving
-70 + 11t + 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'.
-14.28571429 + 2.244897959t + t2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + 2.244897959t + 14.28571429 + t2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + 2.244897959t + t2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + 2.244897959t + t2 = 0 + 14.28571429
2.244897959t + t2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
2.244897959t + t2 = 14.28571429

The t term is 2.244897959t.  Take half its coefficient (1.12244898).
Square it (1.259891713) and add it to both sides.

Add '1.259891713' to each side of the equation.
2.244897959t + 1.259891713 + t2 = 14.28571429 + 1.259891713

Reorder the terms:
1.259891713 + 2.244897959t + t2 = 14.28571429 + 1.259891713

Combine like terms: 14.28571429 + 1.259891713 = 15.545606003
1.259891713 + 2.244897959t + t2 = 15.545606003

Factor a perfect square on the left side:
(t + 1.12244898)(t + 1.12244898) = 15.545606003

Calculate the square root of the right side: 3.942791651

Break this problem into two subproblems by setting 
(t + 1.12244898) equal to 3.942791651 and -3.942791651.


Subproblem 1
t + 1.12244898 = 3.942791651

Simplifying
t + 1.12244898 = 3.942791651

Reorder the terms:
1.12244898 + t = 3.942791651

Solving
1.12244898 + t = 3.942791651

Solving for variable 't'.

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

Add '-1.12244898' to each side of the equation.
1.12244898 + -1.12244898 + t = 3.942791651 + -1.12244898

Combine like terms: 1.12244898 + -1.12244898 = 0.00000000
0.00000000 + t = 3.942791651 + -1.12244898
t = 3.942791651 + -1.12244898

Combine like terms: 3.942791651 + -1.12244898 = 2.820342671
t = 2.820342671

Simplifying
t = 2.820342671


Subproblem 2
t + 1.12244898 = -3.942791651

Simplifying
t + 1.12244898 = -3.942791651

Reorder the terms:
1.12244898 + t = -3.942791651

Solving
1.12244898 + t = -3.942791651

Solving for variable 't'.

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

Add '-1.12244898' to each side of the equation.
1.12244898 + -1.12244898 + t = -3.942791651 + -1.12244898

Combine like terms: 1.12244898 + -1.12244898 = 0.00000000
0.00000000 + t = -3.942791651 + -1.12244898
t = -3.942791651 + -1.12244898

Combine like terms: -3.942791651 + -1.12244898 = -5.065240631
t = -5.065240631

Simplifying
t = -5.065240631


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.820342671, -5.065240631}

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