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Simplifying -4.9t2 + 12t + 600 = 0 Reorder the terms: 600 + 12t + -4.9t2 = 0 Solving 600 + 12t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -122.4489796 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -2.448979592t + 122.4489796 + t2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -2.448979592t + t2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -2.448979592t + t2 = 0 + 122.4489796 -2.448979592t + t2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -2.448979592t + t2 = 122.4489796 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 = 122.4489796 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 122.4489796 + 1.499375261 Combine like terms: 122.4489796 + 1.499375261 = 123.948354861 1.499375261 + -2.448979592t + t2 = 123.948354861 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 123.948354861 Calculate the square root of the right side: 11.133209549 Break this problem into two subproblems by setting (t + -1.224489796) equal to 11.133209549 and -11.133209549.Subproblem 1
t + -1.224489796 = 11.133209549 Simplifying t + -1.224489796 = 11.133209549 Reorder the terms: -1.224489796 + t = 11.133209549 Solving -1.224489796 + t = 11.133209549 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 = 11.133209549 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 11.133209549 + 1.224489796 t = 11.133209549 + 1.224489796 Combine like terms: 11.133209549 + 1.224489796 = 12.357699345 t = 12.357699345 Simplifying t = 12.357699345Subproblem 2
t + -1.224489796 = -11.133209549 Simplifying t + -1.224489796 = -11.133209549 Reorder the terms: -1.224489796 + t = -11.133209549 Solving -1.224489796 + t = -11.133209549 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 = -11.133209549 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -11.133209549 + 1.224489796 t = -11.133209549 + 1.224489796 Combine like terms: -11.133209549 + 1.224489796 = -9.908719753 t = -9.908719753 Simplifying t = -9.908719753Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.357699345, -9.908719753}
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