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Simplifying 0 = -16t2 + 150t + 144 Reorder the terms: 0 = 144 + 150t + -16t2 Solving 0 = 144 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -144 = -144 -144 + -150t + 16t2 = 144 + 150t + -16t2 + -144 + -150t + 16t2 Reorder the terms: -144 + -150t + 16t2 = 144 + -144 + 150t + -150t + -16t2 + 16t2 Combine like terms: 144 + -144 = 0 -144 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -144 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -144 + -150t + 16t2 = 0 + -16t2 + 16t2 -144 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + -75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + -75t + 8t2)' equal to zero and attempt to solve: Simplifying -72 + -75t + 8t2 = 0 Solving -72 + -75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9 + -9.375t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -9.375t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -9.375t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9.375t + t2 = 0 + 9 -9.375t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9.375t + t2 = 9 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 = 9 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 9 + 21.97265625 Combine like terms: 9 + 21.97265625 = 30.97265625 21.97265625 + -9.375t + t2 = 30.97265625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 30.97265625 Calculate the square root of the right side: 5.56530828 Break this problem into two subproblems by setting (t + -4.6875) equal to 5.56530828 and -5.56530828.Subproblem 1
t + -4.6875 = 5.56530828 Simplifying t + -4.6875 = 5.56530828 Reorder the terms: -4.6875 + t = 5.56530828 Solving -4.6875 + t = 5.56530828 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 = 5.56530828 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 5.56530828 + 4.6875 t = 5.56530828 + 4.6875 Combine like terms: 5.56530828 + 4.6875 = 10.25280828 t = 10.25280828 Simplifying t = 10.25280828Subproblem 2
t + -4.6875 = -5.56530828 Simplifying t + -4.6875 = -5.56530828 Reorder the terms: -4.6875 + t = -5.56530828 Solving -4.6875 + t = -5.56530828 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 = -5.56530828 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -5.56530828 + 4.6875 t = -5.56530828 + 4.6875 Combine like terms: -5.56530828 + 4.6875 = -0.87780828 t = -0.87780828 Simplifying t = -0.87780828Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.25280828, -0.87780828}Solution
t = {10.25280828, -0.87780828}
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