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Simplifying 500 = -16t2 + 200t Reorder the terms: 500 = 200t + -16t2 Solving 500 = 200t + -16t2 Solving for variable 't'. Reorder the terms: 500 + -200t + 16t2 = 200t + -200t + -16t2 + 16t2 Combine like terms: 200t + -200t = 0 500 + -200t + 16t2 = 0 + -16t2 + 16t2 500 + -200t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 500 + -200t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(125 + -50t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(125 + -50t + 4t2)' equal to zero and attempt to solve: Simplifying 125 + -50t + 4t2 = 0 Solving 125 + -50t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 31.25 + -12.5t + t2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + -12.5t + -31.25 + t2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + -12.5t + t2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + -12.5t + t2 = 0 + -31.25 -12.5t + t2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 -12.5t + t2 = -31.25 The t term is -12.5t. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5t + 39.0625 + t2 = -31.25 + 39.0625 Reorder the terms: 39.0625 + -12.5t + t2 = -31.25 + 39.0625 Combine like terms: -31.25 + 39.0625 = 7.8125 39.0625 + -12.5t + t2 = 7.8125 Factor a perfect square on the left side: (t + -6.25)(t + -6.25) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (t + -6.25) equal to 2.795084972 and -2.795084972.Subproblem 1
t + -6.25 = 2.795084972 Simplifying t + -6.25 = 2.795084972 Reorder the terms: -6.25 + t = 2.795084972 Solving -6.25 + t = 2.795084972 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 2.795084972 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 2.795084972 + 6.25 t = 2.795084972 + 6.25 Combine like terms: 2.795084972 + 6.25 = 9.045084972 t = 9.045084972 Simplifying t = 9.045084972Subproblem 2
t + -6.25 = -2.795084972 Simplifying t + -6.25 = -2.795084972 Reorder the terms: -6.25 + t = -2.795084972 Solving -6.25 + t = -2.795084972 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -2.795084972 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -2.795084972 + 6.25 t = -2.795084972 + 6.25 Combine like terms: -2.795084972 + 6.25 = 3.454915028 t = 3.454915028 Simplifying t = 3.454915028Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.045084972, 3.454915028}Solution
t = {9.045084972, 3.454915028}
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