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Simplifying 16t2 + 46t + 6 = 0 Reorder the terms: 6 + 46t + 16t2 = 0 Solving 6 + 46t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 23t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 23t + 8t2)' equal to zero and attempt to solve: Simplifying 3 + 23t + 8t2 = 0 Solving 3 + 23t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 2.875t + t2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2.875t + -0.375 + t2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2.875t + t2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2.875t + t2 = 0 + -0.375 2.875t + t2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2.875t + t2 = -0.375 The t term is 2.875t. Take half its coefficient (1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. 2.875t + 2.06640625 + t2 = -0.375 + 2.06640625 Reorder the terms: 2.06640625 + 2.875t + t2 = -0.375 + 2.06640625 Combine like terms: -0.375 + 2.06640625 = 1.69140625 2.06640625 + 2.875t + t2 = 1.69140625 Factor a perfect square on the left side: (t + 1.4375)(t + 1.4375) = 1.69140625 Calculate the square root of the right side: 1.300540753 Break this problem into two subproblems by setting (t + 1.4375) equal to 1.300540753 and -1.300540753.Subproblem 1
t + 1.4375 = 1.300540753 Simplifying t + 1.4375 = 1.300540753 Reorder the terms: 1.4375 + t = 1.300540753 Solving 1.4375 + t = 1.300540753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + t = 1.300540753 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + t = 1.300540753 + -1.4375 t = 1.300540753 + -1.4375 Combine like terms: 1.300540753 + -1.4375 = -0.136959247 t = -0.136959247 Simplifying t = -0.136959247Subproblem 2
t + 1.4375 = -1.300540753 Simplifying t + 1.4375 = -1.300540753 Reorder the terms: 1.4375 + t = -1.300540753 Solving 1.4375 + t = -1.300540753 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4375' to each side of the equation. 1.4375 + -1.4375 + t = -1.300540753 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + t = -1.300540753 + -1.4375 t = -1.300540753 + -1.4375 Combine like terms: -1.300540753 + -1.4375 = -2.738040753 t = -2.738040753 Simplifying t = -2.738040753Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.136959247, -2.738040753}Solution
t = {-0.136959247, -2.738040753}
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