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Simplifying -4.9t2 + 12t + 400 = 0 Reorder the terms: 400 + 12t + -4.9t2 = 0 Solving 400 + 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'. -81.63265306 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '81.63265306' to each side of the equation. -81.63265306 + -2.448979592t + 81.63265306 + t2 = 0 + 81.63265306 Reorder the terms: -81.63265306 + 81.63265306 + -2.448979592t + t2 = 0 + 81.63265306 Combine like terms: -81.63265306 + 81.63265306 = 0.00000000 0.00000000 + -2.448979592t + t2 = 0 + 81.63265306 -2.448979592t + t2 = 0 + 81.63265306 Combine like terms: 0 + 81.63265306 = 81.63265306 -2.448979592t + t2 = 81.63265306 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 = 81.63265306 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 81.63265306 + 1.499375261 Combine like terms: 81.63265306 + 1.499375261 = 83.132028321 1.499375261 + -2.448979592t + t2 = 83.132028321 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 83.132028321 Calculate the square root of the right side: 9.117676695 Break this problem into two subproblems by setting (t + -1.224489796) equal to 9.117676695 and -9.117676695.Subproblem 1
t + -1.224489796 = 9.117676695 Simplifying t + -1.224489796 = 9.117676695 Reorder the terms: -1.224489796 + t = 9.117676695 Solving -1.224489796 + t = 9.117676695 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 = 9.117676695 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 9.117676695 + 1.224489796 t = 9.117676695 + 1.224489796 Combine like terms: 9.117676695 + 1.224489796 = 10.342166491 t = 10.342166491 Simplifying t = 10.342166491Subproblem 2
t + -1.224489796 = -9.117676695 Simplifying t + -1.224489796 = -9.117676695 Reorder the terms: -1.224489796 + t = -9.117676695 Solving -1.224489796 + t = -9.117676695 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 = -9.117676695 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -9.117676695 + 1.224489796 t = -9.117676695 + 1.224489796 Combine like terms: -9.117676695 + 1.224489796 = -7.893186899 t = -7.893186899 Simplifying t = -7.893186899Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.342166491, -7.893186899}
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