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Simplifying 0 = -2000 + 80t + 2t2 Solving 0 = -2000 + 80t + 2t2 Solving for variable 't'. Combine like terms: 0 + 2000 = 2000 2000 + -80t + -2t2 = -2000 + 80t + 2t2 + 2000 + -80t + -2t2 Reorder the terms: 2000 + -80t + -2t2 = -2000 + 2000 + 80t + -80t + 2t2 + -2t2 Combine like terms: -2000 + 2000 = 0 2000 + -80t + -2t2 = 0 + 80t + -80t + 2t2 + -2t2 2000 + -80t + -2t2 = 80t + -80t + 2t2 + -2t2 Combine like terms: 80t + -80t = 0 2000 + -80t + -2t2 = 0 + 2t2 + -2t2 2000 + -80t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 2000 + -80t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1000 + -40t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1000 + -40t + -1t2)' equal to zero and attempt to solve: Simplifying 1000 + -40t + -1t2 = 0 Solving 1000 + -40t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + 40t + t2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 40t + 1000 + t2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 40t + t2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 40t + t2 = 0 + 1000 40t + t2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 40t + t2 = 1000 The t term is 40t. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40t + 400 + t2 = 1000 + 400 Reorder the terms: 400 + 40t + t2 = 1000 + 400 Combine like terms: 1000 + 400 = 1400 400 + 40t + t2 = 1400 Factor a perfect square on the left side: (t + 20)(t + 20) = 1400 Calculate the square root of the right side: 37.416573868 Break this problem into two subproblems by setting (t + 20) equal to 37.416573868 and -37.416573868.Subproblem 1
t + 20 = 37.416573868 Simplifying t + 20 = 37.416573868 Reorder the terms: 20 + t = 37.416573868 Solving 20 + t = 37.416573868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = 37.416573868 + -20 Combine like terms: 20 + -20 = 0 0 + t = 37.416573868 + -20 t = 37.416573868 + -20 Combine like terms: 37.416573868 + -20 = 17.416573868 t = 17.416573868 Simplifying t = 17.416573868Subproblem 2
t + 20 = -37.416573868 Simplifying t + 20 = -37.416573868 Reorder the terms: 20 + t = -37.416573868 Solving 20 + t = -37.416573868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = -37.416573868 + -20 Combine like terms: 20 + -20 = 0 0 + t = -37.416573868 + -20 t = -37.416573868 + -20 Combine like terms: -37.416573868 + -20 = -57.416573868 t = -57.416573868 Simplifying t = -57.416573868Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.416573868, -57.416573868}Solution
t = {17.416573868, -57.416573868}
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