-4.9t^2+180t+2=0

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Solution for -4.9t^2+180t+2=0 equation:


Simplifying
-4.9t2 + 180t + 2 = 0

Reorder the terms:
2 + 180t + -4.9t2 = 0

Solving
2 + 180t + -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'.
-0.4081632653 + -36.73469388t + t2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -36.73469388t + 0.4081632653 + t2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -36.73469388t + t2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -36.73469388t + t2 = 0 + 0.4081632653
-36.73469388t + t2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-36.73469388t + t2 = 0.4081632653

The t term is -36.73469388t.  Take half its coefficient (-18.36734694).
Square it (337.3594336) and add it to both sides.

Add '337.3594336' to each side of the equation.
-36.73469388t + 337.3594336 + t2 = 0.4081632653 + 337.3594336

Reorder the terms:
337.3594336 + -36.73469388t + t2 = 0.4081632653 + 337.3594336

Combine like terms: 0.4081632653 + 337.3594336 = 337.7675968653
337.3594336 + -36.73469388t + t2 = 337.7675968653

Factor a perfect square on the left side:
(t + -18.36734694)(t + -18.36734694) = 337.7675968653

Calculate the square root of the right side: 18.378454692

Break this problem into two subproblems by setting 
(t + -18.36734694) equal to 18.378454692 and -18.378454692.

Subproblem 1

t + -18.36734694 = 18.378454692 Simplifying t + -18.36734694 = 18.378454692 Reorder the terms: -18.36734694 + t = 18.378454692 Solving -18.36734694 + t = 18.378454692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.36734694' to each side of the equation. -18.36734694 + 18.36734694 + t = 18.378454692 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + t = 18.378454692 + 18.36734694 t = 18.378454692 + 18.36734694 Combine like terms: 18.378454692 + 18.36734694 = 36.745801632 t = 36.745801632 Simplifying t = 36.745801632

Subproblem 2

t + -18.36734694 = -18.378454692 Simplifying t + -18.36734694 = -18.378454692 Reorder the terms: -18.36734694 + t = -18.378454692 Solving -18.36734694 + t = -18.378454692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.36734694' to each side of the equation. -18.36734694 + 18.36734694 + t = -18.378454692 + 18.36734694 Combine like terms: -18.36734694 + 18.36734694 = 0.00000000 0.00000000 + t = -18.378454692 + 18.36734694 t = -18.378454692 + 18.36734694 Combine like terms: -18.378454692 + 18.36734694 = -0.011107752 t = -0.011107752 Simplifying t = -0.011107752

Solution

The solution to the problem is based on the solutions from the subproblems. t = {36.745801632, -0.011107752}

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