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Simplifying 4.9t2 + 12t + -56 = 0 Reorder the terms: -56 + 12t + 4.9t2 = 0 Solving -56 + 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'. -11.42857143 + 2.448979592t + t2 = 0 Move the constant term to the right: Add '11.42857143' to each side of the equation. -11.42857143 + 2.448979592t + 11.42857143 + t2 = 0 + 11.42857143 Reorder the terms: -11.42857143 + 11.42857143 + 2.448979592t + t2 = 0 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + 2.448979592t + t2 = 0 + 11.42857143 2.448979592t + t2 = 0 + 11.42857143 Combine like terms: 0 + 11.42857143 = 11.42857143 2.448979592t + t2 = 11.42857143 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 = 11.42857143 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592t + t2 = 11.42857143 + 1.499375261 Combine like terms: 11.42857143 + 1.499375261 = 12.927946691 1.499375261 + 2.448979592t + t2 = 12.927946691 Factor a perfect square on the left side: (t + 1.224489796)(t + 1.224489796) = 12.927946691 Calculate the square root of the right side: 3.595545395 Break this problem into two subproblems by setting (t + 1.224489796) equal to 3.595545395 and -3.595545395.Subproblem 1
t + 1.224489796 = 3.595545395 Simplifying t + 1.224489796 = 3.595545395 Reorder the terms: 1.224489796 + t = 3.595545395 Solving 1.224489796 + t = 3.595545395 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 = 3.595545395 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = 3.595545395 + -1.224489796 t = 3.595545395 + -1.224489796 Combine like terms: 3.595545395 + -1.224489796 = 2.371055599 t = 2.371055599 Simplifying t = 2.371055599Subproblem 2
t + 1.224489796 = -3.595545395 Simplifying t + 1.224489796 = -3.595545395 Reorder the terms: 1.224489796 + t = -3.595545395 Solving 1.224489796 + t = -3.595545395 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 = -3.595545395 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + t = -3.595545395 + -1.224489796 t = -3.595545395 + -1.224489796 Combine like terms: -3.595545395 + -1.224489796 = -4.820035191 t = -4.820035191 Simplifying t = -4.820035191Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.371055599, -4.820035191}
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