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Simplifying -4.9t2 + 12t + 700 = 0 Reorder the terms: 700 + 12t + -4.9t2 = 0 Solving 700 + 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'. -142.8571429 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '142.8571429' to each side of the equation. -142.8571429 + -2.448979592t + 142.8571429 + t2 = 0 + 142.8571429 Reorder the terms: -142.8571429 + 142.8571429 + -2.448979592t + t2 = 0 + 142.8571429 Combine like terms: -142.8571429 + 142.8571429 = 0.0000000 0.0000000 + -2.448979592t + t2 = 0 + 142.8571429 -2.448979592t + t2 = 0 + 142.8571429 Combine like terms: 0 + 142.8571429 = 142.8571429 -2.448979592t + t2 = 142.8571429 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 = 142.8571429 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 142.8571429 + 1.499375261 Combine like terms: 142.8571429 + 1.499375261 = 144.356518161 1.499375261 + -2.448979592t + t2 = 144.356518161 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 144.356518161 Calculate the square root of the right side: 12.01484574 Break this problem into two subproblems by setting (t + -1.224489796) equal to 12.01484574 and -12.01484574.Subproblem 1
t + -1.224489796 = 12.01484574 Simplifying t + -1.224489796 = 12.01484574 Reorder the terms: -1.224489796 + t = 12.01484574 Solving -1.224489796 + t = 12.01484574 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 = 12.01484574 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 12.01484574 + 1.224489796 t = 12.01484574 + 1.224489796 Combine like terms: 12.01484574 + 1.224489796 = 13.239335536 t = 13.239335536 Simplifying t = 13.239335536Subproblem 2
t + -1.224489796 = -12.01484574 Simplifying t + -1.224489796 = -12.01484574 Reorder the terms: -1.224489796 + t = -12.01484574 Solving -1.224489796 + t = -12.01484574 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 = -12.01484574 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -12.01484574 + 1.224489796 t = -12.01484574 + 1.224489796 Combine like terms: -12.01484574 + 1.224489796 = -10.790355944 t = -10.790355944 Simplifying t = -10.790355944Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.239335536, -10.790355944}
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