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Simplifying 0 = 33 + -12t + -4.9t2 Solving 0 = 33 + -12t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -33 = -33 -33 + 12t + 4.9t2 = 33 + -12t + -4.9t2 + -33 + 12t + 4.9t2 Reorder the terms: -33 + 12t + 4.9t2 = 33 + -33 + -12t + 12t + -4.9t2 + 4.9t2 Combine like terms: 33 + -33 = 0 -33 + 12t + 4.9t2 = 0 + -12t + 12t + -4.9t2 + 4.9t2 -33 + 12t + 4.9t2 = -12t + 12t + -4.9t2 + 4.9t2 Combine like terms: -12t + 12t = 0 -33 + 12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -33 + 12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -33 + 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'. -6.734693878 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '6.734693878' to each side of the equation. -6.734693878 + 2.448979592t + 6.734693878 + t2 = 0 + 6.734693878 Reorder the terms: -6.734693878 + 6.734693878 + 2.448979592t + t2 = 0 + 6.734693878 Combine like terms: -6.734693878 + 6.734693878 = 0.000000000 0.000000000 + 2.448979592t + t2 = 0 + 6.734693878 2.448979592t + t2 = 0 + 6.734693878 Combine like terms: 0 + 6.734693878 = 6.734693878 2.448979592t + t2 = 6.734693878 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 = 6.734693878 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = 6.734693878 + 1.499375261 Combine like terms: 6.734693878 + 1.499375261 = 8.234069139 1.499375261 + 2.448979592t + t2 = 8.234069139 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 8.234069139 Calculate the square root of the right side: 2.869506776 Break this problem into two subproblems by setting (t + 1.224489796) equal to 2.869506776 and -2.869506776.Subproblem 1
t + 1.224489796 = 2.869506776 Simplifying t + 1.224489796 = 2.869506776 Reorder the terms: 1.224489796 + t = 2.869506776 Solving 1.224489796 + t = 2.869506776 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 = 2.869506776 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 2.869506776 + -1.224489796 t = 2.869506776 + -1.224489796 Combine like terms: 2.869506776 + -1.224489796 = 1.64501698 t = 1.64501698 Simplifying t = 1.64501698Subproblem 2
t + 1.224489796 = -2.869506776 Simplifying t + 1.224489796 = -2.869506776 Reorder the terms: 1.224489796 + t = -2.869506776 Solving 1.224489796 + t = -2.869506776 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 = -2.869506776 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -2.869506776 + -1.224489796 t = -2.869506776 + -1.224489796 Combine like terms: -2.869506776 + -1.224489796 = -4.093996572 t = -4.093996572 Simplifying t = -4.093996572Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.64501698, -4.093996572}
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