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Simplifying 16t2 + 150t + 20 = 0 Reorder the terms: 20 + 150t + 16t2 = 0 Solving 20 + 150t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 75t + 8t2)' equal to zero and attempt to solve: Simplifying 10 + 75t + 8t2 = 0 Solving 10 + 75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.25 + 9.375t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 9.375t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 9.375t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 9.375t + t2 = 0 + -1.25 9.375t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 9.375t + t2 = -1.25 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 = -1.25 + 21.97265625 Reorder the terms: 21.97265625 + 9.375t + t2 = -1.25 + 21.97265625 Combine like terms: -1.25 + 21.97265625 = 20.72265625 21.97265625 + 9.375t + t2 = 20.72265625 Factor a perfect square on the left side: (t + 4.6875)(t + 4.6875) = 20.72265625 Calculate the square root of the right side: 4.552214434 Break this problem into two subproblems by setting (t + 4.6875) equal to 4.552214434 and -4.552214434.Subproblem 1
t + 4.6875 = 4.552214434 Simplifying t + 4.6875 = 4.552214434 Reorder the terms: 4.6875 + t = 4.552214434 Solving 4.6875 + t = 4.552214434 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 = 4.552214434 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = 4.552214434 + -4.6875 t = 4.552214434 + -4.6875 Combine like terms: 4.552214434 + -4.6875 = -0.135285566 t = -0.135285566 Simplifying t = -0.135285566Subproblem 2
t + 4.6875 = -4.552214434 Simplifying t + 4.6875 = -4.552214434 Reorder the terms: 4.6875 + t = -4.552214434 Solving 4.6875 + t = -4.552214434 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 = -4.552214434 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = -4.552214434 + -4.6875 t = -4.552214434 + -4.6875 Combine like terms: -4.552214434 + -4.6875 = -9.239714434 t = -9.239714434 Simplifying t = -9.239714434Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.135285566, -9.239714434}Solution
t = {-0.135285566, -9.239714434}
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