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Simplifying 16t2 + 12t + -182 = 0 Reorder the terms: -182 + 12t + 16t2 = 0 Solving -182 + 12t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-91 + 6t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-91 + 6t + 8t2)' equal to zero and attempt to solve: Simplifying -91 + 6t + 8t2 = 0 Solving -91 + 6t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.375 + 0.75t + t2 = 0 Move the constant term to the right: Add '11.375' to each side of the equation. -11.375 + 0.75t + 11.375 + t2 = 0 + 11.375 Reorder the terms: -11.375 + 11.375 + 0.75t + t2 = 0 + 11.375 Combine like terms: -11.375 + 11.375 = 0.000 0.000 + 0.75t + t2 = 0 + 11.375 0.75t + t2 = 0 + 11.375 Combine like terms: 0 + 11.375 = 11.375 0.75t + t2 = 11.375 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 11.375 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 11.375 + 0.140625 Combine like terms: 11.375 + 0.140625 = 11.515625 0.140625 + 0.75t + t2 = 11.515625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 11.515625 Calculate the square root of the right side: 3.39346799 Break this problem into two subproblems by setting (t + 0.375) equal to 3.39346799 and -3.39346799.Subproblem 1
t + 0.375 = 3.39346799 Simplifying t + 0.375 = 3.39346799 Reorder the terms: 0.375 + t = 3.39346799 Solving 0.375 + t = 3.39346799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 3.39346799 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 3.39346799 + -0.375 t = 3.39346799 + -0.375 Combine like terms: 3.39346799 + -0.375 = 3.01846799 t = 3.01846799 Simplifying t = 3.01846799Subproblem 2
t + 0.375 = -3.39346799 Simplifying t + 0.375 = -3.39346799 Reorder the terms: 0.375 + t = -3.39346799 Solving 0.375 + t = -3.39346799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -3.39346799 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -3.39346799 + -0.375 t = -3.39346799 + -0.375 Combine like terms: -3.39346799 + -0.375 = -3.76846799 t = -3.76846799 Simplifying t = -3.76846799Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.01846799, -3.76846799}Solution
t = {3.01846799, -3.76846799}
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