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Simplifying -4.9t2 + 12t + 300 = 0 Reorder the terms: 300 + 12t + -4.9t2 = 0 Solving 300 + 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'. -61.2244898 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -2.448979592t + 61.2244898 + t2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -2.448979592t + t2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -2.448979592t + t2 = 0 + 61.2244898 -2.448979592t + t2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -2.448979592t + t2 = 61.2244898 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 = 61.2244898 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 61.2244898 + 1.499375261 Combine like terms: 61.2244898 + 1.499375261 = 62.723865061 1.499375261 + -2.448979592t + t2 = 62.723865061 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 62.723865061 Calculate the square root of the right side: 7.919839964 Break this problem into two subproblems by setting (t + -1.224489796) equal to 7.919839964 and -7.919839964.Subproblem 1
t + -1.224489796 = 7.919839964 Simplifying t + -1.224489796 = 7.919839964 Reorder the terms: -1.224489796 + t = 7.919839964 Solving -1.224489796 + t = 7.919839964 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 = 7.919839964 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 7.919839964 + 1.224489796 t = 7.919839964 + 1.224489796 Combine like terms: 7.919839964 + 1.224489796 = 9.14432976 t = 9.14432976 Simplifying t = 9.14432976Subproblem 2
t + -1.224489796 = -7.919839964 Simplifying t + -1.224489796 = -7.919839964 Reorder the terms: -1.224489796 + t = -7.919839964 Solving -1.224489796 + t = -7.919839964 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 = -7.919839964 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -7.919839964 + 1.224489796 t = -7.919839964 + 1.224489796 Combine like terms: -7.919839964 + 1.224489796 = -6.695350168 t = -6.695350168 Simplifying t = -6.695350168Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.14432976, -6.695350168}
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