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Simplifying 0 = -16t2 + -18t + 210 Reorder the terms: 0 = 210 + -18t + -16t2 Solving 0 = 210 + -18t + -16t2 Solving for variable 't'. Combine like terms: 0 + -210 = -210 -210 + 18t + 16t2 = 210 + -18t + -16t2 + -210 + 18t + 16t2 Reorder the terms: -210 + 18t + 16t2 = 210 + -210 + -18t + 18t + -16t2 + 16t2 Combine like terms: 210 + -210 = 0 -210 + 18t + 16t2 = 0 + -18t + 18t + -16t2 + 16t2 -210 + 18t + 16t2 = -18t + 18t + -16t2 + 16t2 Combine like terms: -18t + 18t = 0 -210 + 18t + 16t2 = 0 + -16t2 + 16t2 -210 + 18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -210 + 18t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-105 + 9t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-105 + 9t + 8t2)' equal to zero and attempt to solve: Simplifying -105 + 9t + 8t2 = 0 Solving -105 + 9t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -13.125 + 1.125t + t2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + 1.125t + 13.125 + t2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + 1.125t + t2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + 1.125t + t2 = 0 + 13.125 1.125t + t2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 1.125t + t2 = 13.125 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 = 13.125 + 0.31640625 Reorder the terms: 0.31640625 + 1.125t + t2 = 13.125 + 0.31640625 Combine like terms: 13.125 + 0.31640625 = 13.44140625 0.31640625 + 1.125t + t2 = 13.44140625 Factor a perfect square on the left side: (t + 0.5625)(t + 0.5625) = 13.44140625 Calculate the square root of the right side: 3.666252344 Break this problem into two subproblems by setting (t + 0.5625) equal to 3.666252344 and -3.666252344.Subproblem 1
t + 0.5625 = 3.666252344 Simplifying t + 0.5625 = 3.666252344 Reorder the terms: 0.5625 + t = 3.666252344 Solving 0.5625 + t = 3.666252344 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 = 3.666252344 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = 3.666252344 + -0.5625 t = 3.666252344 + -0.5625 Combine like terms: 3.666252344 + -0.5625 = 3.103752344 t = 3.103752344 Simplifying t = 3.103752344Subproblem 2
t + 0.5625 = -3.666252344 Simplifying t + 0.5625 = -3.666252344 Reorder the terms: 0.5625 + t = -3.666252344 Solving 0.5625 + t = -3.666252344 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 = -3.666252344 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = -3.666252344 + -0.5625 t = -3.666252344 + -0.5625 Combine like terms: -3.666252344 + -0.5625 = -4.228752344 t = -4.228752344 Simplifying t = -4.228752344Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.103752344, -4.228752344}Solution
t = {3.103752344, -4.228752344}
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