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Simplifying 0 = -4.9t2 + 24t + -13 Reorder the terms: 0 = -13 + 24t + -4.9t2 Solving 0 = -13 + 24t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + 13 = 13 13 + -24t + 4.9t2 = -13 + 24t + -4.9t2 + 13 + -24t + 4.9t2 Reorder the terms: 13 + -24t + 4.9t2 = -13 + 13 + 24t + -24t + -4.9t2 + 4.9t2 Combine like terms: -13 + 13 = 0 13 + -24t + 4.9t2 = 0 + 24t + -24t + -4.9t2 + 4.9t2 13 + -24t + 4.9t2 = 24t + -24t + -4.9t2 + 4.9t2 Combine like terms: 24t + -24t = 0 13 + -24t + 4.9t2 = 0 + -4.9t2 + 4.9t2 13 + -24t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 13 + -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'. 2.653061224 + -4.897959184t + t2 = 0 Move the constant term to the right: Add '-2.653061224' to each side of the equation. 2.653061224 + -4.897959184t + -2.653061224 + t2 = 0 + -2.653061224 Reorder the terms: 2.653061224 + -2.653061224 + -4.897959184t + t2 = 0 + -2.653061224 Combine like terms: 2.653061224 + -2.653061224 = 0.000000000 0.000000000 + -4.897959184t + t2 = 0 + -2.653061224 -4.897959184t + t2 = 0 + -2.653061224 Combine like terms: 0 + -2.653061224 = -2.653061224 -4.897959184t + t2 = -2.653061224 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 = -2.653061224 + 5.997501042 Reorder the terms: 5.997501042 + -4.897959184t + t2 = -2.653061224 + 5.997501042 Combine like terms: -2.653061224 + 5.997501042 = 3.344439818 5.997501042 + -4.897959184t + t2 = 3.344439818 Factor a perfect square on the left side: (t + -2.448979592)(t + -2.448979592) = 3.344439818 Calculate the square root of the right side: 1.828780965 Break this problem into two subproblems by setting (t + -2.448979592) equal to 1.828780965 and -1.828780965.Subproblem 1
t + -2.448979592 = 1.828780965 Simplifying t + -2.448979592 = 1.828780965 Reorder the terms: -2.448979592 + t = 1.828780965 Solving -2.448979592 + t = 1.828780965 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 = 1.828780965 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = 1.828780965 + 2.448979592 t = 1.828780965 + 2.448979592 Combine like terms: 1.828780965 + 2.448979592 = 4.277760557 t = 4.277760557 Simplifying t = 4.277760557Subproblem 2
t + -2.448979592 = -1.828780965 Simplifying t + -2.448979592 = -1.828780965 Reorder the terms: -2.448979592 + t = -1.828780965 Solving -2.448979592 + t = -1.828780965 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 = -1.828780965 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + t = -1.828780965 + 2.448979592 t = -1.828780965 + 2.448979592 Combine like terms: -1.828780965 + 2.448979592 = 0.620198627 t = 0.620198627 Simplifying t = 0.620198627Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.277760557, 0.620198627}
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