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Simplifying -80 = 12t + -4.9t2 Solving -80 = 12t + -4.9t2 Solving for variable 't'. Reorder the terms: -80 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 12t + -12t = 0 -80 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -80 + -12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -80 + -12t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -16.32653061 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '16.32653061' to each side of the equation. -16.32653061 + -2.448979592t + 16.32653061 + t2 = 0 + 16.32653061 Reorder the terms: -16.32653061 + 16.32653061 + -2.448979592t + t2 = 0 + 16.32653061 Combine like terms: -16.32653061 + 16.32653061 = 0.00000000 0.00000000 + -2.448979592t + t2 = 0 + 16.32653061 -2.448979592t + t2 = 0 + 16.32653061 Combine like terms: 0 + 16.32653061 = 16.32653061 -2.448979592t + t2 = 16.32653061 The t term is -2.448979592t. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592t + 1.499375261 + t2 = 16.32653061 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 16.32653061 + 1.499375261 Combine like terms: 16.32653061 + 1.499375261 = 17.825905871 1.499375261 + -2.448979592t + t2 = 17.825905871 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 17.825905871 Calculate the square root of the right side: 4.222073646 Break this problem into two subproblems by setting (t + -1.224489796) equal to 4.222073646 and -4.222073646.Subproblem 1
t + -1.224489796 = 4.222073646 Simplifying t + -1.224489796 = 4.222073646 Reorder the terms: -1.224489796 + t = 4.222073646 Solving -1.224489796 + t = 4.222073646 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = 4.222073646 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 4.222073646 + 1.224489796 t = 4.222073646 + 1.224489796 Combine like terms: 4.222073646 + 1.224489796 = 5.446563442 t = 5.446563442 Simplifying t = 5.446563442Subproblem 2
t + -1.224489796 = -4.222073646 Simplifying t + -1.224489796 = -4.222073646 Reorder the terms: -1.224489796 + t = -4.222073646 Solving -1.224489796 + t = -4.222073646 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + t = -4.222073646 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -4.222073646 + 1.224489796 t = -4.222073646 + 1.224489796 Combine like terms: -4.222073646 + 1.224489796 = -2.99758385 t = -2.99758385 Simplifying t = -2.99758385Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.446563442, -2.99758385}
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