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Simplifying 0 = -16t2 + 110t + 2 Reorder the terms: 0 = 2 + 110t + -16t2 Solving 0 = 2 + 110t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -110t + 16t2 = 2 + 110t + -16t2 + -2 + -110t + 16t2 Reorder the terms: -2 + -110t + 16t2 = 2 + -2 + 110t + -110t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -110t + 16t2 = 0 + 110t + -110t + -16t2 + 16t2 -2 + -110t + 16t2 = 110t + -110t + -16t2 + 16t2 Combine like terms: 110t + -110t = 0 -2 + -110t + 16t2 = 0 + -16t2 + 16t2 -2 + -110t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -110t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -55t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -55t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -55t + 8t2 = 0 Solving -1 + -55t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -6.875t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -6.875t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -6.875t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -6.875t + t2 = 0 + 0.125 -6.875t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -6.875t + t2 = 0.125 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 = 0.125 + 11.81640625 Reorder the terms: 11.81640625 + -6.875t + t2 = 0.125 + 11.81640625 Combine like terms: 0.125 + 11.81640625 = 11.94140625 11.81640625 + -6.875t + t2 = 11.94140625 Factor a perfect square on the left side: (t + -3.4375)(t + -3.4375) = 11.94140625 Calculate the square root of the right side: 3.455633987 Break this problem into two subproblems by setting (t + -3.4375) equal to 3.455633987 and -3.455633987.Subproblem 1
t + -3.4375 = 3.455633987 Simplifying t + -3.4375 = 3.455633987 Reorder the terms: -3.4375 + t = 3.455633987 Solving -3.4375 + t = 3.455633987 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 = 3.455633987 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = 3.455633987 + 3.4375 t = 3.455633987 + 3.4375 Combine like terms: 3.455633987 + 3.4375 = 6.893133987 t = 6.893133987 Simplifying t = 6.893133987Subproblem 2
t + -3.4375 = -3.455633987 Simplifying t + -3.4375 = -3.455633987 Reorder the terms: -3.4375 + t = -3.455633987 Solving -3.4375 + t = -3.455633987 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 = -3.455633987 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + t = -3.455633987 + 3.4375 t = -3.455633987 + 3.4375 Combine like terms: -3.455633987 + 3.4375 = -0.018133987 t = -0.018133987 Simplifying t = -0.018133987Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.893133987, -0.018133987}Solution
t = {6.893133987, -0.018133987}
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