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Simplifying -4.9t2 + 4t + 12 = 0 Reorder the terms: 12 + 4t + -4.9t2 = 0 Solving 12 + 4t + -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'. -2.448979592 + -0.8163265306t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -0.8163265306t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -0.8163265306t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -0.8163265306t + t2 = 0 + 2.448979592 -0.8163265306t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -0.8163265306t + t2 = 2.448979592 The t term is -0.8163265306t. Take half its coefficient (-0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. -0.8163265306t + 0.1665972511 + t2 = 2.448979592 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306t + t2 = 2.448979592 + 0.1665972511 Combine like terms: 2.448979592 + 0.1665972511 = 2.6155768431 0.1665972511 + -0.8163265306t + t2 = 2.6155768431 Factor a perfect square on the left side: (t + -0.4081632653)(t + -0.4081632653) = 2.6155768431 Calculate the square root of the right side: 1.617274511 Break this problem into two subproblems by setting (t + -0.4081632653) equal to 1.617274511 and -1.617274511.Subproblem 1
t + -0.4081632653 = 1.617274511 Simplifying t + -0.4081632653 = 1.617274511 Reorder the terms: -0.4081632653 + t = 1.617274511 Solving -0.4081632653 + t = 1.617274511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + t = 1.617274511 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = 1.617274511 + 0.4081632653 t = 1.617274511 + 0.4081632653 Combine like terms: 1.617274511 + 0.4081632653 = 2.0254377763 t = 2.0254377763 Simplifying t = 2.0254377763Subproblem 2
t + -0.4081632653 = -1.617274511 Simplifying t + -0.4081632653 = -1.617274511 Reorder the terms: -0.4081632653 + t = -1.617274511 Solving -0.4081632653 + t = -1.617274511 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + t = -1.617274511 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = -1.617274511 + 0.4081632653 t = -1.617274511 + 0.4081632653 Combine like terms: -1.617274511 + 0.4081632653 = -1.2091112457 t = -1.2091112457 Simplifying t = -1.2091112457Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.0254377763, -1.2091112457}
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