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Simplifying 0 = -4.9t2 + 12t + 1.5 Reorder the terms: 0 = 1.5 + 12t + -4.9t2 Solving 0 = 1.5 + 12t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1.5 = -1.5 -1.5 + -12t + 4.9t2 = 1.5 + 12t + -4.9t2 + -1.5 + -12t + 4.9t2 Reorder the terms: -1.5 + -12t + 4.9t2 = 1.5 + -1.5 + 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -12t + 4.9t2 = 0.0 + 12t + -12t + -4.9t2 + 4.9t2 -1.5 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 12t + -12t = 0 -1.5 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -1.5 + -12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1.5 + -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'. -0.306122449 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -2.448979592t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -2.448979592t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -2.448979592t + t2 = 0 + 0.306122449 -2.448979592t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -2.448979592t + t2 = 0.306122449 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 = 0.306122449 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 0.306122449 + 1.499375261 Combine like terms: 0.306122449 + 1.499375261 = 1.80549771 1.499375261 + -2.448979592t + t2 = 1.80549771 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 1.80549771 Calculate the square root of the right side: 1.3436881 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.3436881 and -1.3436881.Subproblem 1
t + -1.224489796 = 1.3436881 Simplifying t + -1.224489796 = 1.3436881 Reorder the terms: -1.224489796 + t = 1.3436881 Solving -1.224489796 + t = 1.3436881 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 = 1.3436881 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.3436881 + 1.224489796 t = 1.3436881 + 1.224489796 Combine like terms: 1.3436881 + 1.224489796 = 2.568177896 t = 2.568177896 Simplifying t = 2.568177896Subproblem 2
t + -1.224489796 = -1.3436881 Simplifying t + -1.224489796 = -1.3436881 Reorder the terms: -1.224489796 + t = -1.3436881 Solving -1.224489796 + t = -1.3436881 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 = -1.3436881 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.3436881 + 1.224489796 t = -1.3436881 + 1.224489796 Combine like terms: -1.3436881 + 1.224489796 = -0.119198304 t = -0.119198304 Simplifying t = -0.119198304Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.568177896, -0.119198304}
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