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Simplifying -4.9t2 + 24t + 44 = 11 Reorder the terms: 44 + 24t + -4.9t2 = 11 Solving 44 + 24t + -4.9t2 = 11 Solving for variable 't'. Reorder the terms: 44 + -11 + 24t + -4.9t2 = 11 + -11 Combine like terms: 44 + -11 = 33 33 + 24t + -4.9t2 = 11 + -11 Combine like terms: 11 + -11 = 0 33 + 24t + -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'. -6.734693878 + -4.897959184t + t2 = 0 Move the constant term to the right: Add '6.734693878' to each side of the equation. -6.734693878 + -4.897959184t + 6.734693878 + t2 = 0 + 6.734693878 Reorder the terms: -6.734693878 + 6.734693878 + -4.897959184t + t2 = 0 + 6.734693878 Combine like terms: -6.734693878 + 6.734693878 = 0.000000000 0.000000000 + -4.897959184t + t2 = 0 + 6.734693878 -4.897959184t + t2 = 0 + 6.734693878 Combine like terms: 0 + 6.734693878 = 6.734693878 -4.897959184t + t2 = 6.734693878 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 = 6.734693878 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184t + t2 = 6.734693878 + 5.997501042 Combine like terms: 6.734693878 + 5.997501042 = 12.73219492 5.997501042 + -4.897959184t + t2 = 12.73219492 Factor a perfect square on the left side: (t + -2.448979592)(t + -2.448979592) = 12.73219492 Calculate the square root of the right side: 3.568220133 Break this problem into two subproblems by setting (t + -2.448979592) equal to 3.568220133 and -3.568220133.Subproblem 1
t + -2.448979592 = 3.568220133 Simplifying t + -2.448979592 = 3.568220133 Reorder the terms: -2.448979592 + t = 3.568220133 Solving -2.448979592 + t = 3.568220133 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 = 3.568220133 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = 3.568220133 + 2.448979592 t = 3.568220133 + 2.448979592 Combine like terms: 3.568220133 + 2.448979592 = 6.017199725 t = 6.017199725 Simplifying t = 6.017199725Subproblem 2
t + -2.448979592 = -3.568220133 Simplifying t + -2.448979592 = -3.568220133 Reorder the terms: -2.448979592 + t = -3.568220133 Solving -2.448979592 + t = -3.568220133 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 = -3.568220133 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = -3.568220133 + 2.448979592 t = -3.568220133 + 2.448979592 Combine like terms: -3.568220133 + 2.448979592 = -1.119240541 t = -1.119240541 Simplifying t = -1.119240541Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.017199725, -1.119240541}
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