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Simplifying 16t2 + 76t + 46 = 0 Reorder the terms: 46 + 76t + 16t2 = 0 Solving 46 + 76t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(23 + 38t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + 38t + 8t2)' equal to zero and attempt to solve: Simplifying 23 + 38t + 8t2 = 0 Solving 23 + 38t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.875 + 4.75t + t2 = 0 Move the constant term to the right: Add '-2.875' to each side of the equation. 2.875 + 4.75t + -2.875 + t2 = 0 + -2.875 Reorder the terms: 2.875 + -2.875 + 4.75t + t2 = 0 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + 4.75t + t2 = 0 + -2.875 4.75t + t2 = 0 + -2.875 Combine like terms: 0 + -2.875 = -2.875 4.75t + t2 = -2.875 The t term is 4.75t. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75t + 5.640625 + t2 = -2.875 + 5.640625 Reorder the terms: 5.640625 + 4.75t + t2 = -2.875 + 5.640625 Combine like terms: -2.875 + 5.640625 = 2.765625 5.640625 + 4.75t + t2 = 2.765625 Factor a perfect square on the left side: (t + 2.375)(t + 2.375) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (t + 2.375) equal to 1.663016837 and -1.663016837.Subproblem 1
t + 2.375 = 1.663016837 Simplifying t + 2.375 = 1.663016837 Reorder the terms: 2.375 + t = 1.663016837 Solving 2.375 + t = 1.663016837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = 1.663016837 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = 1.663016837 + -2.375 t = 1.663016837 + -2.375 Combine like terms: 1.663016837 + -2.375 = -0.711983163 t = -0.711983163 Simplifying t = -0.711983163Subproblem 2
t + 2.375 = -1.663016837 Simplifying t + 2.375 = -1.663016837 Reorder the terms: 2.375 + t = -1.663016837 Solving 2.375 + t = -1.663016837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = -1.663016837 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = -1.663016837 + -2.375 t = -1.663016837 + -2.375 Combine like terms: -1.663016837 + -2.375 = -4.038016837 t = -4.038016837 Simplifying t = -4.038016837Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.711983163, -4.038016837}Solution
t = {-0.711983163, -4.038016837}
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