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Simplifying 0 = 15 + 12t + -4.9t2 Solving 0 = 15 + 12t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -12t + 4.9t2 = 15 + 12t + -4.9t2 + -15 + -12t + 4.9t2 Reorder the terms: -15 + -12t + 4.9t2 = 15 + -15 + 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 15 + -15 = 0 -15 + -12t + 4.9t2 = 0 + 12t + -12t + -4.9t2 + 4.9t2 -15 + -12t + 4.9t2 = 12t + -12t + -4.9t2 + 4.9t2 Combine like terms: 12t + -12t = 0 -15 + -12t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -15 + -12t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -15 + -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'. -3.06122449 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -2.448979592t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -2.448979592t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -2.448979592t + t2 = 0 + 3.06122449 -2.448979592t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -2.448979592t + t2 = 3.06122449 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 = 3.06122449 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 3.06122449 + 1.499375261 Combine like terms: 3.06122449 + 1.499375261 = 4.560599751 1.499375261 + -2.448979592t + t2 = 4.560599751 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 4.560599751 Calculate the square root of the right side: 2.135556075 Break this problem into two subproblems by setting (t + -1.224489796) equal to 2.135556075 and -2.135556075.Subproblem 1
t + -1.224489796 = 2.135556075 Simplifying t + -1.224489796 = 2.135556075 Reorder the terms: -1.224489796 + t = 2.135556075 Solving -1.224489796 + t = 2.135556075 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 = 2.135556075 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 2.135556075 + 1.224489796 t = 2.135556075 + 1.224489796 Combine like terms: 2.135556075 + 1.224489796 = 3.360045871 t = 3.360045871 Simplifying t = 3.360045871Subproblem 2
t + -1.224489796 = -2.135556075 Simplifying t + -1.224489796 = -2.135556075 Reorder the terms: -1.224489796 + t = -2.135556075 Solving -1.224489796 + t = -2.135556075 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 = -2.135556075 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -2.135556075 + 1.224489796 t = -2.135556075 + 1.224489796 Combine like terms: -2.135556075 + 1.224489796 = -0.911066279 t = -0.911066279 Simplifying t = -0.911066279Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.360045871, -0.911066279}
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