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Simplifying 0(t) = -16t2 + 60t + 1250 Anything times zero is zero. 0t = -16t2 + 60t + 1250 Reorder the terms: 0 = 1250 + 60t + -16t2 Solving 0 = 1250 + 60t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1250 = -1250 -1250 + -60t + 16t2 = 1250 + 60t + -16t2 + -1250 + -60t + 16t2 Reorder the terms: -1250 + -60t + 16t2 = 1250 + -1250 + 60t + -60t + -16t2 + 16t2 Combine like terms: 1250 + -1250 = 0 -1250 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 -1250 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 -1250 + -60t + 16t2 = 0 + -16t2 + 16t2 -1250 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1250 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-625 + -30t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-625 + -30t + 8t2)' equal to zero and attempt to solve: Simplifying -625 + -30t + 8t2 = 0 Solving -625 + -30t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -78.125 + -3.75t + t2 = 0 Move the constant term to the right: Add '78.125' to each side of the equation. -78.125 + -3.75t + 78.125 + t2 = 0 + 78.125 Reorder the terms: -78.125 + 78.125 + -3.75t + t2 = 0 + 78.125 Combine like terms: -78.125 + 78.125 = 0.000 0.000 + -3.75t + t2 = 0 + 78.125 -3.75t + t2 = 0 + 78.125 Combine like terms: 0 + 78.125 = 78.125 -3.75t + t2 = 78.125 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 78.125 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 78.125 + 3.515625 Combine like terms: 78.125 + 3.515625 = 81.640625 3.515625 + -3.75t + t2 = 81.640625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 81.640625 Calculate the square root of the right side: 9.035520184 Break this problem into two subproblems by setting (t + -1.875) equal to 9.035520184 and -9.035520184.Subproblem 1
t + -1.875 = 9.035520184 Simplifying t + -1.875 = 9.035520184 Reorder the terms: -1.875 + t = 9.035520184 Solving -1.875 + t = 9.035520184 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 9.035520184 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 9.035520184 + 1.875 t = 9.035520184 + 1.875 Combine like terms: 9.035520184 + 1.875 = 10.910520184 t = 10.910520184 Simplifying t = 10.910520184Subproblem 2
t + -1.875 = -9.035520184 Simplifying t + -1.875 = -9.035520184 Reorder the terms: -1.875 + t = -9.035520184 Solving -1.875 + t = -9.035520184 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -9.035520184 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -9.035520184 + 1.875 t = -9.035520184 + 1.875 Combine like terms: -9.035520184 + 1.875 = -7.160520184 t = -7.160520184 Simplifying t = -7.160520184Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.910520184, -7.160520184}Solution
t = {10.910520184, -7.160520184}
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