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Simplifying 1000 + -0.15t2 + -45t = 0 Reorder the terms: 1000 + -45t + -0.15t2 = 0 Solving 1000 + -45t + -0.15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.15 the coefficient of the squared term: Divide each side by '-0.15'. -6666.666667 + 300t + t2 = 0 Move the constant term to the right: Add '6666.666667' to each side of the equation. -6666.666667 + 300t + 6666.666667 + t2 = 0 + 6666.666667 Reorder the terms: -6666.666667 + 6666.666667 + 300t + t2 = 0 + 6666.666667 Combine like terms: -6666.666667 + 6666.666667 = 0.000000 0.000000 + 300t + t2 = 0 + 6666.666667 300t + t2 = 0 + 6666.666667 Combine like terms: 0 + 6666.666667 = 6666.666667 300t + t2 = 6666.666667 The t term is 300t. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300t + 22500 + t2 = 6666.666667 + 22500 Reorder the terms: 22500 + 300t + t2 = 6666.666667 + 22500 Combine like terms: 6666.666667 + 22500 = 29166.666667 22500 + 300t + t2 = 29166.666667 Factor a perfect square on the left side: (t + 150)(t + 150) = 29166.666667 Calculate the square root of the right side: 170.782512767 Break this problem into two subproblems by setting (t + 150) equal to 170.782512767 and -170.782512767.Subproblem 1
t + 150 = 170.782512767 Simplifying t + 150 = 170.782512767 Reorder the terms: 150 + t = 170.782512767 Solving 150 + t = 170.782512767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + t = 170.782512767 + -150 Combine like terms: 150 + -150 = 0 0 + t = 170.782512767 + -150 t = 170.782512767 + -150 Combine like terms: 170.782512767 + -150 = 20.782512767 t = 20.782512767 Simplifying t = 20.782512767Subproblem 2
t + 150 = -170.782512767 Simplifying t + 150 = -170.782512767 Reorder the terms: 150 + t = -170.782512767 Solving 150 + t = -170.782512767 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + t = -170.782512767 + -150 Combine like terms: 150 + -150 = 0 0 + t = -170.782512767 + -150 t = -170.782512767 + -150 Combine like terms: -170.782512767 + -150 = -320.782512767 t = -320.782512767 Simplifying t = -320.782512767Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.782512767, -320.782512767}
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