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Simplifying 0 = -16t2 + 18t + 18 Reorder the terms: 0 = 18 + 18t + -16t2 Solving 0 = 18 + 18t + -16t2 Solving for variable 't'. Combine like terms: 0 + -18 = -18 -18 + -18t + 16t2 = 18 + 18t + -16t2 + -18 + -18t + 16t2 Reorder the terms: -18 + -18t + 16t2 = 18 + -18 + 18t + -18t + -16t2 + 16t2 Combine like terms: 18 + -18 = 0 -18 + -18t + 16t2 = 0 + 18t + -18t + -16t2 + 16t2 -18 + -18t + 16t2 = 18t + -18t + -16t2 + 16t2 Combine like terms: 18t + -18t = 0 -18 + -18t + 16t2 = 0 + -16t2 + 16t2 -18 + -18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -18 + -18t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -9t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -9t + 8t2)' equal to zero and attempt to solve: Simplifying -9 + -9t + 8t2 = 0 Solving -9 + -9t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -1.125t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1.125t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1.125t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1.125t + t2 = 0 + 1.125 -1.125t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1.125t + t2 = 1.125 The t term is -1.125t. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125t + 0.31640625 + t2 = 1.125 + 0.31640625 Reorder the terms: 0.31640625 + -1.125t + t2 = 1.125 + 0.31640625 Combine like terms: 1.125 + 0.31640625 = 1.44140625 0.31640625 + -1.125t + t2 = 1.44140625 Factor a perfect square on the left side: (t + -0.5625)(t + -0.5625) = 1.44140625 Calculate the square root of the right side: 1.200585795 Break this problem into two subproblems by setting (t + -0.5625) equal to 1.200585795 and -1.200585795.Subproblem 1
t + -0.5625 = 1.200585795 Simplifying t + -0.5625 = 1.200585795 Reorder the terms: -0.5625 + t = 1.200585795 Solving -0.5625 + t = 1.200585795 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = 1.200585795 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = 1.200585795 + 0.5625 t = 1.200585795 + 0.5625 Combine like terms: 1.200585795 + 0.5625 = 1.763085795 t = 1.763085795 Simplifying t = 1.763085795Subproblem 2
t + -0.5625 = -1.200585795 Simplifying t + -0.5625 = -1.200585795 Reorder the terms: -0.5625 + t = -1.200585795 Solving -0.5625 + t = -1.200585795 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = -1.200585795 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = -1.200585795 + 0.5625 t = -1.200585795 + 0.5625 Combine like terms: -1.200585795 + 0.5625 = -0.638085795 t = -0.638085795 Simplifying t = -0.638085795Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.763085795, -0.638085795}Solution
t = {1.763085795, -0.638085795}
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