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Simplifying 2000 + -80t + 0.25t2 = 0 Solving 2000 + -80t + 0.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 8000 + -320t + t2 = 0 Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + -320t + -8000 + t2 = 0 + -8000 Reorder the terms: 8000 + -8000 + -320t + t2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -320t + t2 = 0 + -8000 -320t + t2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 -320t + t2 = -8000 The t term is -320t. Take half its coefficient (-160). Square it (25600) and add it to both sides. Add '25600' to each side of the equation. -320t + 25600 + t2 = -8000 + 25600 Reorder the terms: 25600 + -320t + t2 = -8000 + 25600 Combine like terms: -8000 + 25600 = 17600 25600 + -320t + t2 = 17600 Factor a perfect square on the left side: (t + -160)(t + -160) = 17600 Calculate the square root of the right side: 132.664991614 Break this problem into two subproblems by setting (t + -160) equal to 132.664991614 and -132.664991614.Subproblem 1
t + -160 = 132.664991614 Simplifying t + -160 = 132.664991614 Reorder the terms: -160 + t = 132.664991614 Solving -160 + t = 132.664991614 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '160' to each side of the equation. -160 + 160 + t = 132.664991614 + 160 Combine like terms: -160 + 160 = 0 0 + t = 132.664991614 + 160 t = 132.664991614 + 160 Combine like terms: 132.664991614 + 160 = 292.664991614 t = 292.664991614 Simplifying t = 292.664991614Subproblem 2
t + -160 = -132.664991614 Simplifying t + -160 = -132.664991614 Reorder the terms: -160 + t = -132.664991614 Solving -160 + t = -132.664991614 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '160' to each side of the equation. -160 + 160 + t = -132.664991614 + 160 Combine like terms: -160 + 160 = 0 0 + t = -132.664991614 + 160 t = -132.664991614 + 160 Combine like terms: -132.664991614 + 160 = 27.335008386 t = 27.335008386 Simplifying t = 27.335008386Solution
The solution to the problem is based on the solutions from the subproblems. t = {292.664991614, 27.335008386}
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