-4.9t^2+6t+70=0

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Solution for -4.9t^2+6t+70=0 equation:


Simplifying
-4.9t2 + 6t + 70 = 0

Reorder the terms:
70 + 6t + -4.9t2 = 0

Solving
70 + 6t + -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 + -1.224489796t + t2 = 0

Move the constant term to the right:

Add '14.28571429' to each side of the equation.
-14.28571429 + -1.224489796t + 14.28571429 + t2 = 0 + 14.28571429

Reorder the terms:
-14.28571429 + 14.28571429 + -1.224489796t + t2 = 0 + 14.28571429

Combine like terms: -14.28571429 + 14.28571429 = 0.00000000
0.00000000 + -1.224489796t + t2 = 0 + 14.28571429
-1.224489796t + t2 = 0 + 14.28571429

Combine like terms: 0 + 14.28571429 = 14.28571429
-1.224489796t + t2 = 14.28571429

The t term is -1.224489796t.  Take half its coefficient (-0.612244898).
Square it (0.3748438151) and add it to both sides.

Add '0.3748438151' to each side of the equation.
-1.224489796t + 0.3748438151 + t2 = 14.28571429 + 0.3748438151

Reorder the terms:
0.3748438151 + -1.224489796t + t2 = 14.28571429 + 0.3748438151

Combine like terms: 14.28571429 + 0.3748438151 = 14.6605581051
0.3748438151 + -1.224489796t + t2 = 14.6605581051

Factor a perfect square on the left side:
(t + -0.612244898)(t + -0.612244898) = 14.6605581051

Calculate the square root of the right side: 3.828910825

Break this problem into two subproblems by setting 
(t + -0.612244898) equal to 3.828910825 and -3.828910825.

Subproblem 1

t + -0.612244898 = 3.828910825 Simplifying t + -0.612244898 = 3.828910825 Reorder the terms: -0.612244898 + t = 3.828910825 Solving -0.612244898 + t = 3.828910825 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = 3.828910825 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 3.828910825 + 0.612244898 t = 3.828910825 + 0.612244898 Combine like terms: 3.828910825 + 0.612244898 = 4.441155723 t = 4.441155723 Simplifying t = 4.441155723

Subproblem 2

t + -0.612244898 = -3.828910825 Simplifying t + -0.612244898 = -3.828910825 Reorder the terms: -0.612244898 + t = -3.828910825 Solving -0.612244898 + t = -3.828910825 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = -3.828910825 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -3.828910825 + 0.612244898 t = -3.828910825 + 0.612244898 Combine like terms: -3.828910825 + 0.612244898 = -3.216665927 t = -3.216665927 Simplifying t = -3.216665927

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.441155723, -3.216665927}

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