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Simplifying -16t2 + 110t + 6 = 0 Reorder the terms: 6 + 110t + -16t2 = 0 Solving 6 + 110t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 55t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 55t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 55t + -8t2 = 0 Solving 3 + 55t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -6.875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -6.875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -6.875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -6.875t + t2 = 0 + 0.375 -6.875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -6.875t + t2 = 0.375 The t term is -6.875t. Take half its coefficient (-3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. -6.875t + 11.81640625 + t2 = 0.375 + 11.81640625 Reorder the terms: 11.81640625 + -6.875t + t2 = 0.375 + 11.81640625 Combine like terms: 0.375 + 11.81640625 = 12.19140625 11.81640625 + -6.875t + t2 = 12.19140625 Factor a perfect square on the left side: (t + -3.4375)(t + -3.4375) = 12.19140625 Calculate the square root of the right side: 3.491619431 Break this problem into two subproblems by setting (t + -3.4375) equal to 3.491619431 and -3.491619431.Subproblem 1
t + -3.4375 = 3.491619431 Simplifying t + -3.4375 = 3.491619431 Reorder the terms: -3.4375 + t = 3.491619431 Solving -3.4375 + t = 3.491619431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + t = 3.491619431 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = 3.491619431 + 3.4375 t = 3.491619431 + 3.4375 Combine like terms: 3.491619431 + 3.4375 = 6.929119431 t = 6.929119431 Simplifying t = 6.929119431Subproblem 2
t + -3.4375 = -3.491619431 Simplifying t + -3.4375 = -3.491619431 Reorder the terms: -3.4375 + t = -3.491619431 Solving -3.4375 + t = -3.491619431 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.4375' to each side of the equation. -3.4375 + 3.4375 + t = -3.491619431 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = -3.491619431 + 3.4375 t = -3.491619431 + 3.4375 Combine like terms: -3.491619431 + 3.4375 = -0.054119431 t = -0.054119431 Simplifying t = -0.054119431Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.929119431, -0.054119431}Solution
t = {6.929119431, -0.054119431}
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