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Simplifying 0 = -16t2 + 150t + 500 Reorder the terms: 0 = 500 + 150t + -16t2 Solving 0 = 500 + 150t + -16t2 Solving for variable 't'. Combine like terms: 0 + -500 = -500 -500 + -150t + 16t2 = 500 + 150t + -16t2 + -500 + -150t + 16t2 Reorder the terms: -500 + -150t + 16t2 = 500 + -500 + 150t + -150t + -16t2 + 16t2 Combine like terms: 500 + -500 = 0 -500 + -150t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -500 + -150t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -500 + -150t + 16t2 = 0 + -16t2 + 16t2 -500 + -150t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -500 + -150t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + -75t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + -75t + 8t2)' equal to zero and attempt to solve: Simplifying -250 + -75t + 8t2 = 0 Solving -250 + -75t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -31.25 + -9.375t + t2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + -9.375t + 31.25 + t2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + -9.375t + t2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + -9.375t + t2 = 0 + 31.25 -9.375t + t2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 -9.375t + t2 = 31.25 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 = 31.25 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 31.25 + 21.97265625 Combine like terms: 31.25 + 21.97265625 = 53.22265625 21.97265625 + -9.375t + t2 = 53.22265625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 53.22265625 Calculate the square root of the right side: 7.295385956 Break this problem into two subproblems by setting (t + -4.6875) equal to 7.295385956 and -7.295385956.Subproblem 1
t + -4.6875 = 7.295385956 Simplifying t + -4.6875 = 7.295385956 Reorder the terms: -4.6875 + t = 7.295385956 Solving -4.6875 + t = 7.295385956 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 = 7.295385956 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 7.295385956 + 4.6875 t = 7.295385956 + 4.6875 Combine like terms: 7.295385956 + 4.6875 = 11.982885956 t = 11.982885956 Simplifying t = 11.982885956Subproblem 2
t + -4.6875 = -7.295385956 Simplifying t + -4.6875 = -7.295385956 Reorder the terms: -4.6875 + t = -7.295385956 Solving -4.6875 + t = -7.295385956 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 = -7.295385956 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -7.295385956 + 4.6875 t = -7.295385956 + 4.6875 Combine like terms: -7.295385956 + 4.6875 = -2.607885956 t = -2.607885956 Simplifying t = -2.607885956Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.982885956, -2.607885956}Solution
t = {11.982885956, -2.607885956}
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