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Simplifying 30 = 12t + 4.9t2 Solving 30 = 12t + 4.9t2 Solving for variable 't'. Reorder the terms: 30 + -12t + -4.9t2 = 12t + -12t + 4.9t2 + -4.9t2 Combine like terms: 12t + -12t = 0 30 + -12t + -4.9t2 = 0 + 4.9t2 + -4.9t2 30 + -12t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 30 + -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'. -6.12244898 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + 2.448979592t + 6.12244898 + t2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + 2.448979592t + t2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + 2.448979592t + t2 = 0 + 6.12244898 2.448979592t + t2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 2.448979592t + t2 = 6.12244898 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 = 6.12244898 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = 6.12244898 + 1.499375261 Combine like terms: 6.12244898 + 1.499375261 = 7.621824241 1.499375261 + 2.448979592t + t2 = 7.621824241 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 7.621824241 Calculate the square root of the right side: 2.760765155 Break this problem into two subproblems by setting (t + 1.224489796) equal to 2.760765155 and -2.760765155.Subproblem 1
t + 1.224489796 = 2.760765155 Simplifying t + 1.224489796 = 2.760765155 Reorder the terms: 1.224489796 + t = 2.760765155 Solving 1.224489796 + t = 2.760765155 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 = 2.760765155 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 2.760765155 + -1.224489796 t = 2.760765155 + -1.224489796 Combine like terms: 2.760765155 + -1.224489796 = 1.536275359 t = 1.536275359 Simplifying t = 1.536275359Subproblem 2
t + 1.224489796 = -2.760765155 Simplifying t + 1.224489796 = -2.760765155 Reorder the terms: 1.224489796 + t = -2.760765155 Solving 1.224489796 + t = -2.760765155 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 = -2.760765155 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -2.760765155 + -1.224489796 t = -2.760765155 + -1.224489796 Combine like terms: -2.760765155 + -1.224489796 = -3.985254951 t = -3.985254951 Simplifying t = -3.985254951Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.536275359, -3.985254951}
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