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Simplifying 0 = 4.9t2 + -24t + 2 Reorder the terms: 0 = 2 + -24t + 4.9t2 Solving 0 = 2 + -24t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + 24t + -4.9t2 = 2 + -24t + 4.9t2 + -2 + 24t + -4.9t2 Reorder the terms: -2 + 24t + -4.9t2 = 2 + -2 + -24t + 24t + 4.9t2 + -4.9t2 Combine like terms: 2 + -2 = 0 -2 + 24t + -4.9t2 = 0 + -24t + 24t + 4.9t2 + -4.9t2 -2 + 24t + -4.9t2 = -24t + 24t + 4.9t2 + -4.9t2 Combine like terms: -24t + 24t = 0 -2 + 24t + -4.9t2 = 0 + 4.9t2 + -4.9t2 -2 + 24t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -2 + 24t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.4081632653 + -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 = 5.5893377767 5.997501042 + -4.897959184t + t2 = 5.5893377767 Factor a perfect square on the left side: (t + -2.448979592)(t + -2.448979592) = 5.5893377767 Calculate the square root of the right side: 2.364178034 Break this problem into two subproblems by setting (t + -2.448979592) equal to 2.364178034 and -2.364178034.Subproblem 1
t + -2.448979592 = 2.364178034 Simplifying t + -2.448979592 = 2.364178034 Reorder the terms: -2.448979592 + t = 2.364178034 Solving -2.448979592 + t = 2.364178034 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 = 2.364178034 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = 2.364178034 + 2.448979592 t = 2.364178034 + 2.448979592 Combine like terms: 2.364178034 + 2.448979592 = 4.813157626 t = 4.813157626 Simplifying t = 4.813157626Subproblem 2
t + -2.448979592 = -2.364178034 Simplifying t + -2.448979592 = -2.364178034 Reorder the terms: -2.448979592 + t = -2.364178034 Solving -2.448979592 + t = -2.364178034 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 = -2.364178034 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = -2.364178034 + 2.448979592 t = -2.364178034 + 2.448979592 Combine like terms: -2.364178034 + 2.448979592 = 0.084801558 t = 0.084801558 Simplifying t = 0.084801558Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.813157626, 0.084801558}
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