4.9t^2-12t-65=0

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Solution for 4.9t^2-12t-65=0 equation:


Simplifying
4.9t2 + -12t + -65 = 0

Reorder the terms:
-65 + -12t + 4.9t2 = 0

Solving
-65 + -12t + 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'.
-13.26530612 + -2.448979592t + t2 = 0

Move the constant term to the right:

Add '13.26530612' to each side of the equation.
-13.26530612 + -2.448979592t + 13.26530612 + t2 = 0 + 13.26530612

Reorder the terms:
-13.26530612 + 13.26530612 + -2.448979592t + t2 = 0 + 13.26530612

Combine like terms: -13.26530612 + 13.26530612 = 0.00000000
0.00000000 + -2.448979592t + t2 = 0 + 13.26530612
-2.448979592t + t2 = 0 + 13.26530612

Combine like terms: 0 + 13.26530612 = 13.26530612
-2.448979592t + t2 = 13.26530612

The t term is -2.448979592t.  Take half its coefficient (-1.224489796).
Square it (1.499375261) and add it to both sides.

Add '1.499375261' to each side of the equation.
-2.448979592t + 1.499375261 + t2 = 13.26530612 + 1.499375261

Reorder the terms:
1.499375261 + -2.448979592t + t2 = 13.26530612 + 1.499375261

Combine like terms: 13.26530612 + 1.499375261 = 14.764681381
1.499375261 + -2.448979592t + t2 = 14.764681381

Factor a perfect square on the left side:
(t + -1.224489796)(t + -1.224489796) = 14.764681381

Calculate the square root of the right side: 3.842483752

Break this problem into two subproblems by setting 
(t + -1.224489796) equal to 3.842483752 and -3.842483752.

Subproblem 1

t + -1.224489796 = 3.842483752 Simplifying t + -1.224489796 = 3.842483752 Reorder the terms: -1.224489796 + t = 3.842483752 Solving -1.224489796 + t = 3.842483752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 3.842483752 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 3.842483752 + 1.224489796 t = 3.842483752 + 1.224489796 Combine like terms: 3.842483752 + 1.224489796 = 5.066973548 t = 5.066973548 Simplifying t = 5.066973548

Subproblem 2

t + -1.224489796 = -3.842483752 Simplifying t + -1.224489796 = -3.842483752 Reorder the terms: -1.224489796 + t = -3.842483752 Solving -1.224489796 + t = -3.842483752 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -3.842483752 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -3.842483752 + 1.224489796 t = -3.842483752 + 1.224489796 Combine like terms: -3.842483752 + 1.224489796 = -2.617993956 t = -2.617993956 Simplifying t = -2.617993956

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.066973548, -2.617993956}

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