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Simplifying 16t2 + 1000 = 400t Reorder the terms: 1000 + 16t2 = 400t Solving 1000 + 16t2 = 400t Solving for variable 't'. Reorder the terms: 1000 + -400t + 16t2 = 400t + -400t Combine like terms: 400t + -400t = 0 1000 + -400t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(125 + -50t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(125 + -50t + 2t2)' equal to zero and attempt to solve: Simplifying 125 + -50t + 2t2 = 0 Solving 125 + -50t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 62.5 + -25t + t2 = 0 Move the constant term to the right: Add '-62.5' to each side of the equation. 62.5 + -25t + -62.5 + t2 = 0 + -62.5 Reorder the terms: 62.5 + -62.5 + -25t + t2 = 0 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + -25t + t2 = 0 + -62.5 -25t + t2 = 0 + -62.5 Combine like terms: 0 + -62.5 = -62.5 -25t + t2 = -62.5 The t term is -25t. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25t + 156.25 + t2 = -62.5 + 156.25 Reorder the terms: 156.25 + -25t + t2 = -62.5 + 156.25 Combine like terms: -62.5 + 156.25 = 93.75 156.25 + -25t + t2 = 93.75 Factor a perfect square on the left side: (t + -12.5)(t + -12.5) = 93.75 Calculate the square root of the right side: 9.682458366 Break this problem into two subproblems by setting (t + -12.5) equal to 9.682458366 and -9.682458366.Subproblem 1
t + -12.5 = 9.682458366 Simplifying t + -12.5 = 9.682458366 Reorder the terms: -12.5 + t = 9.682458366 Solving -12.5 + t = 9.682458366 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = 9.682458366 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = 9.682458366 + 12.5 t = 9.682458366 + 12.5 Combine like terms: 9.682458366 + 12.5 = 22.182458366 t = 22.182458366 Simplifying t = 22.182458366Subproblem 2
t + -12.5 = -9.682458366 Simplifying t + -12.5 = -9.682458366 Reorder the terms: -12.5 + t = -9.682458366 Solving -12.5 + t = -9.682458366 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + t = -9.682458366 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + t = -9.682458366 + 12.5 t = -9.682458366 + 12.5 Combine like terms: -9.682458366 + 12.5 = 2.817541634 t = 2.817541634 Simplifying t = 2.817541634Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.182458366, 2.817541634}Solution
t = {22.182458366, 2.817541634}
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