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Simplifying 2 + 24t + -4.9t2 = 0 Solving 2 + 24t + -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'. -0.4081632653 + -4.897959184t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -4.897959184t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -4.897959184t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -4.897959184t + t2 = 0 + 0.4081632653 -4.897959184t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -4.897959184t + t2 = 0.4081632653 The t term is -4.897959184t. Take half its coefficient (-2.448979592). Square it (5.997501042) and add it to both sides. Add '5.997501042' to each side of the equation. -4.897959184t + 5.997501042 + t2 = 0.4081632653 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184t + t2 = 0.4081632653 + 5.997501042 Combine like terms: 0.4081632653 + 5.997501042 = 6.4056643073 5.997501042 + -4.897959184t + t2 = 6.4056643073 Factor a perfect square on the left side: (t + -2.448979592)(t + -2.448979592) = 6.4056643073 Calculate the square root of the right side: 2.530941388 Break this problem into two subproblems by setting (t + -2.448979592) equal to 2.530941388 and -2.530941388.Subproblem 1
t + -2.448979592 = 2.530941388 Simplifying t + -2.448979592 = 2.530941388 Reorder the terms: -2.448979592 + t = 2.530941388 Solving -2.448979592 + t = 2.530941388 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + t = 2.530941388 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = 2.530941388 + 2.448979592 t = 2.530941388 + 2.448979592 Combine like terms: 2.530941388 + 2.448979592 = 4.97992098 t = 4.97992098 Simplifying t = 4.97992098Subproblem 2
t + -2.448979592 = -2.530941388 Simplifying t + -2.448979592 = -2.530941388 Reorder the terms: -2.448979592 + t = -2.530941388 Solving -2.448979592 + t = -2.530941388 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.448979592' to each side of the equation. -2.448979592 + 2.448979592 + t = -2.530941388 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = -2.530941388 + 2.448979592 t = -2.530941388 + 2.448979592 Combine like terms: -2.530941388 + 2.448979592 = -0.081961796 t = -0.081961796 Simplifying t = -0.081961796Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.97992098, -0.081961796}
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