(.5*-9.8t^2)+(189t)=295

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Solution for (.5*-9.8t^2)+(189t)=295 equation:


Simplifying
(0.5 * -9.8t2) + (189t) = 295

Multiply 0.5 * -9.8
(-4.9t2) + (189t) = 295

Reorder the terms:
(189t) + (-4.9t2) = 295

Solving
(189t) + (-4.9t2) = 295

Solving for variable 't'.

Reorder the terms:
-295 + (189t) + (-4.9t2) = 295 + -295

Combine like terms: 295 + -295 = 0
-295 + (189t) + (-4.9t2) = 0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
60.20408163 + (-38.57142857t) + t2 = 0

Move the constant term to the right:

Add '-60.20408163' to each side of the equation.
60.20408163 + (-38.57142857t) + -60.20408163 + t2 = 0 + -60.20408163

Reorder the terms:
60.20408163 + -60.20408163 + (-38.57142857t) + t2 = 0 + -60.20408163

Combine like terms: 60.20408163 + -60.20408163 = 0.00000000
0.00000000 + (-38.57142857t) + t2 = 0 + -60.20408163
(-38.57142857t) + t2 = 0 + -60.20408163

Combine like terms: 0 + -60.20408163 = -60.20408163
(-38.57142857t) + t2 = -60.20408163

The t term is (-38.57142857t).  Take half its coefficient (-19.28571429).
Square it (371.9387757) and add it to both sides.

Add '371.9387757' to each side of the equation.
(-38.57142857t) + 371.9387757 + t2 = -60.20408163 + 371.9387757

Reorder the terms:
371.9387757 + (-38.57142857t) + t2 = -60.20408163 + 371.9387757

Combine like terms: -60.20408163 + 371.9387757 = 311.73469407
371.9387757 + (-38.57142857t) + t2 = 311.73469407

Factor a perfect square on the left side:
((t) + -19.28571429)((t) + -19.28571429) = 311.73469407

Calculate the square root of the right side: 17.65601014

Break this problem into two subproblems by setting 
((t) + -19.28571429) equal to 17.65601014 and -17.65601014.

Subproblem 1

(t) + -19.28571429 = 17.65601014 Simplifying (t) + -19.28571429 = 17.65601014 t + -19.28571429 = 17.65601014 Reorder the terms: -19.28571429 + t = 17.65601014 Solving -19.28571429 + t = 17.65601014 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '19.28571429' to each side of the equation. -19.28571429 + 19.28571429 + t = 17.65601014 + 19.28571429 Combine like terms: -19.28571429 + 19.28571429 = 0.00000000 0.00000000 + t = 17.65601014 + 19.28571429 t = 17.65601014 + 19.28571429 Combine like terms: 17.65601014 + 19.28571429 = 36.94172443 t = 36.94172443 Simplifying t = 36.94172443

Subproblem 2

(t) + -19.28571429 = -17.65601014 Simplifying (t) + -19.28571429 = -17.65601014 t + -19.28571429 = -17.65601014 Reorder the terms: -19.28571429 + t = -17.65601014 Solving -19.28571429 + t = -17.65601014 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '19.28571429' to each side of the equation. -19.28571429 + 19.28571429 + t = -17.65601014 + 19.28571429 Combine like terms: -19.28571429 + 19.28571429 = 0.00000000 0.00000000 + t = -17.65601014 + 19.28571429 t = -17.65601014 + 19.28571429 Combine like terms: -17.65601014 + 19.28571429 = 1.62970415 t = 1.62970415 Simplifying t = 1.62970415

Solution

The solution to the problem is based on the solutions from the subproblems. t = {36.94172443, 1.62970415}

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