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Simplifying 4.9t2 + -12t = 2 Reorder the terms: -12t + 4.9t2 = 2 Solving -12t + 4.9t2 = 2 Solving for variable 't'. Reorder the terms: -2 + -12t + 4.9t2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -12t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.4081632653 + -2.448979592t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -2.448979592t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -2.448979592t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -2.448979592t + t2 = 0 + 0.4081632653 -2.448979592t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -2.448979592t + t2 = 0.4081632653 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 = 0.4081632653 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592t + t2 = 0.4081632653 + 1.499375261 Combine like terms: 0.4081632653 + 1.499375261 = 1.9075385263 1.499375261 + -2.448979592t + t2 = 1.9075385263 Factor a perfect square on the left side: (t + -1.224489796)(t + -1.224489796) = 1.9075385263 Calculate the square root of the right side: 1.381136679 Break this problem into two subproblems by setting (t + -1.224489796) equal to 1.381136679 and -1.381136679.Subproblem 1
t + -1.224489796 = 1.381136679 Simplifying t + -1.224489796 = 1.381136679 Reorder the terms: -1.224489796 + t = 1.381136679 Solving -1.224489796 + t = 1.381136679 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 = 1.381136679 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = 1.381136679 + 1.224489796 t = 1.381136679 + 1.224489796 Combine like terms: 1.381136679 + 1.224489796 = 2.605626475 t = 2.605626475 Simplifying t = 2.605626475Subproblem 2
t + -1.224489796 = -1.381136679 Simplifying t + -1.224489796 = -1.381136679 Reorder the terms: -1.224489796 + t = -1.381136679 Solving -1.224489796 + t = -1.381136679 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 = -1.381136679 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + t = -1.381136679 + 1.224489796 t = -1.381136679 + 1.224489796 Combine like terms: -1.381136679 + 1.224489796 = -0.156646883 t = -0.156646883 Simplifying t = -0.156646883Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.605626475, -0.156646883}
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