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Simplifying 4.905t2 + -7.625t + 0.65 = 0 Reorder the terms: 0.65 + -7.625t + 4.905t2 = 0 Solving 0.65 + -7.625t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 0.1325178389 + -1.554536188t + t2 = 0 Move the constant term to the right: Add '-0.1325178389' to each side of the equation. 0.1325178389 + -1.554536188t + -0.1325178389 + t2 = 0 + -0.1325178389 Reorder the terms: 0.1325178389 + -0.1325178389 + -1.554536188t + t2 = 0 + -0.1325178389 Combine like terms: 0.1325178389 + -0.1325178389 = 0.0000000000 0.0000000000 + -1.554536188t + t2 = 0 + -0.1325178389 -1.554536188t + t2 = 0 + -0.1325178389 Combine like terms: 0 + -0.1325178389 = -0.1325178389 -1.554536188t + t2 = -0.1325178389 The t term is -1.554536188t. Take half its coefficient (-0.777268094). Square it (0.6041456900) and add it to both sides. Add '0.6041456900' to each side of the equation. -1.554536188t + 0.6041456900 + t2 = -0.1325178389 + 0.6041456900 Reorder the terms: 0.6041456900 + -1.554536188t + t2 = -0.1325178389 + 0.6041456900 Combine like terms: -0.1325178389 + 0.6041456900 = 0.4716278511 0.6041456900 + -1.554536188t + t2 = 0.4716278511 Factor a perfect square on the left side: (t + -0.777268094)(t + -0.777268094) = 0.4716278511 Calculate the square root of the right side: 0.686751666 Break this problem into two subproblems by setting (t + -0.777268094) equal to 0.686751666 and -0.686751666.Subproblem 1
t + -0.777268094 = 0.686751666 Simplifying t + -0.777268094 = 0.686751666 Reorder the terms: -0.777268094 + t = 0.686751666 Solving -0.777268094 + t = 0.686751666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.777268094' to each side of the equation. -0.777268094 + 0.777268094 + t = 0.686751666 + 0.777268094 Combine like terms: -0.777268094 + 0.777268094 = 0.000000000 0.000000000 + t = 0.686751666 + 0.777268094 t = 0.686751666 + 0.777268094 Combine like terms: 0.686751666 + 0.777268094 = 1.46401976 t = 1.46401976 Simplifying t = 1.46401976Subproblem 2
t + -0.777268094 = -0.686751666 Simplifying t + -0.777268094 = -0.686751666 Reorder the terms: -0.777268094 + t = -0.686751666 Solving -0.777268094 + t = -0.686751666 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.777268094' to each side of the equation. -0.777268094 + 0.777268094 + t = -0.686751666 + 0.777268094 Combine like terms: -0.777268094 + 0.777268094 = 0.000000000 0.000000000 + t = -0.686751666 + 0.777268094 t = -0.686751666 + 0.777268094 Combine like terms: -0.686751666 + 0.777268094 = 0.090516428 t = 0.090516428 Simplifying t = 0.090516428Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.46401976, 0.090516428}
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