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Simplifying 0.83t2 + -7t + 10 = 0 Reorder the terms: 10 + -7t + 0.83t2 = 0 Solving 10 + -7t + 0.83t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 12.04819277 + -8.43373494t + t2 = 0 Move the constant term to the right: Add '-12.04819277' to each side of the equation. 12.04819277 + -8.43373494t + -12.04819277 + t2 = 0 + -12.04819277 Reorder the terms: 12.04819277 + -12.04819277 + -8.43373494t + t2 = 0 + -12.04819277 Combine like terms: 12.04819277 + -12.04819277 = 0.00000000 0.00000000 + -8.43373494t + t2 = 0 + -12.04819277 -8.43373494t + t2 = 0 + -12.04819277 Combine like terms: 0 + -12.04819277 = -12.04819277 -8.43373494t + t2 = -12.04819277 The t term is -8.43373494t. Take half its coefficient (-4.21686747). Square it (17.78197126) and add it to both sides. Add '17.78197126' to each side of the equation. -8.43373494t + 17.78197126 + t2 = -12.04819277 + 17.78197126 Reorder the terms: 17.78197126 + -8.43373494t + t2 = -12.04819277 + 17.78197126 Combine like terms: -12.04819277 + 17.78197126 = 5.73377849 17.78197126 + -8.43373494t + t2 = 5.73377849 Factor a perfect square on the left side: (t + -4.21686747)(t + -4.21686747) = 5.73377849 Calculate the square root of the right side: 2.394530954 Break this problem into two subproblems by setting (t + -4.21686747) equal to 2.394530954 and -2.394530954.Subproblem 1
t + -4.21686747 = 2.394530954 Simplifying t + -4.21686747 = 2.394530954 Reorder the terms: -4.21686747 + t = 2.394530954 Solving -4.21686747 + t = 2.394530954 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21686747' to each side of the equation. -4.21686747 + 4.21686747 + t = 2.394530954 + 4.21686747 Combine like terms: -4.21686747 + 4.21686747 = 0.00000000 0.00000000 + t = 2.394530954 + 4.21686747 t = 2.394530954 + 4.21686747 Combine like terms: 2.394530954 + 4.21686747 = 6.611398424 t = 6.611398424 Simplifying t = 6.611398424Subproblem 2
t + -4.21686747 = -2.394530954 Simplifying t + -4.21686747 = -2.394530954 Reorder the terms: -4.21686747 + t = -2.394530954 Solving -4.21686747 + t = -2.394530954 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21686747' to each side of the equation. -4.21686747 + 4.21686747 + t = -2.394530954 + 4.21686747 Combine like terms: -4.21686747 + 4.21686747 = 0.00000000 0.00000000 + t = -2.394530954 + 4.21686747 t = -2.394530954 + 4.21686747 Combine like terms: -2.394530954 + 4.21686747 = 1.822336516 t = 1.822336516 Simplifying t = 1.822336516Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.611398424, 1.822336516}
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