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Simplifying 10 = -16t2 + 150t + 30 Reorder the terms: 10 = 30 + 150t + -16t2 Solving 10 = 30 + 150t + -16t2 Solving for variable 't'. Combine like terms: 10 + -30 = -20 -20 + -150t + 16t2 = 30 + 150t + -16t2 + -30 + -150t + 16t2 Reorder the terms: -20 + -150t + 16t2 = 30 + -30 + 150t + -150t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 -20 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -20 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -20 + -150t + 16t2 = 0 + -16t2 + 16t2 -20 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -150t + 16t2 = 0 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 = 23.22265625 21.97265625 + -9.375t + t2 = 23.22265625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 23.22265625 Calculate the square root of the right side: 4.818989132 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.818989132 and -4.818989132.Subproblem 1
t + -4.6875 = 4.818989132 Simplifying t + -4.6875 = 4.818989132 Reorder the terms: -4.6875 + t = 4.818989132 Solving -4.6875 + t = 4.818989132 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 = 4.818989132 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.818989132 + 4.6875 t = 4.818989132 + 4.6875 Combine like terms: 4.818989132 + 4.6875 = 9.506489132 t = 9.506489132 Simplifying t = 9.506489132Subproblem 2
t + -4.6875 = -4.818989132 Simplifying t + -4.6875 = -4.818989132 Reorder the terms: -4.6875 + t = -4.818989132 Solving -4.6875 + t = -4.818989132 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 = -4.818989132 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.818989132 + 4.6875 t = -4.818989132 + 4.6875 Combine like terms: -4.818989132 + 4.6875 = -0.131489132 t = -0.131489132 Simplifying t = -0.131489132Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.506489132, -0.131489132}Solution
t = {9.506489132, -0.131489132}
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