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Simplifying 34 = 150t + -16t2 Solving 34 = 150t + -16t2 Solving for variable 't'. Reorder the terms: 34 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 34 + -150t + 16t2 = 0 + -16t2 + 16t2 34 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 34 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -75t + 8t2)' equal to zero and attempt to solve: Simplifying 17 + -75t + 8t2 = 0 Solving 17 + -75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.125 + -9.375t + t2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -9.375t + -2.125 + t2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -9.375t + t2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -9.375t + t2 = 0 + -2.125 -9.375t + t2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -9.375t + t2 = -2.125 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = -2.125 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = -2.125 + 21.97265625 Combine like terms: -2.125 + 21.97265625 = 19.84765625 21.97265625 + -9.375t + t2 = 19.84765625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 19.84765625 Calculate the square root of the right side: 4.455070847 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.455070847 and -4.455070847.Subproblem 1
t + -4.6875 = 4.455070847 Simplifying t + -4.6875 = 4.455070847 Reorder the terms: -4.6875 + t = 4.455070847 Solving -4.6875 + t = 4.455070847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 4.455070847 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.455070847 + 4.6875 t = 4.455070847 + 4.6875 Combine like terms: 4.455070847 + 4.6875 = 9.142570847 t = 9.142570847 Simplifying t = 9.142570847Subproblem 2
t + -4.6875 = -4.455070847 Simplifying t + -4.6875 = -4.455070847 Reorder the terms: -4.6875 + t = -4.455070847 Solving -4.6875 + t = -4.455070847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -4.455070847 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.455070847 + 4.6875 t = -4.455070847 + 4.6875 Combine like terms: -4.455070847 + 4.6875 = 0.232429153 t = 0.232429153 Simplifying t = 0.232429153Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.142570847, 0.232429153}Solution
t = {9.142570847, 0.232429153}
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