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Simplifying -0.0492x2 + 0.7172x + -2.4583 = 0 Reorder the terms: -2.4583 + 0.7172x + -0.0492x2 = 0 Solving -2.4583 + 0.7172x + -0.0492x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0492 the coefficient of the squared term: Divide each side by '-0.0492'. 49.96544715 + -14.57723577x + x2 = 0 Move the constant term to the right: Add '-49.96544715' to each side of the equation. 49.96544715 + -14.57723577x + -49.96544715 + x2 = 0 + -49.96544715 Reorder the terms: 49.96544715 + -49.96544715 + -14.57723577x + x2 = 0 + -49.96544715 Combine like terms: 49.96544715 + -49.96544715 = 0.00000000 0.00000000 + -14.57723577x + x2 = 0 + -49.96544715 -14.57723577x + x2 = 0 + -49.96544715 Combine like terms: 0 + -49.96544715 = -49.96544715 -14.57723577x + x2 = -49.96544715 The x term is -14.57723577x. Take half its coefficient (-7.288617885). Square it (53.12395067) and add it to both sides. Add '53.12395067' to each side of the equation. -14.57723577x + 53.12395067 + x2 = -49.96544715 + 53.12395067 Reorder the terms: 53.12395067 + -14.57723577x + x2 = -49.96544715 + 53.12395067 Combine like terms: -49.96544715 + 53.12395067 = 3.15850352 53.12395067 + -14.57723577x + x2 = 3.15850352 Factor a perfect square on the left side: (x + -7.288617885)(x + -7.288617885) = 3.15850352 Calculate the square root of the right side: 1.777217916 Break this problem into two subproblems by setting (x + -7.288617885) equal to 1.777217916 and -1.777217916.Subproblem 1
x + -7.288617885 = 1.777217916 Simplifying x + -7.288617885 = 1.777217916 Reorder the terms: -7.288617885 + x = 1.777217916 Solving -7.288617885 + x = 1.777217916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.288617885' to each side of the equation. -7.288617885 + 7.288617885 + x = 1.777217916 + 7.288617885 Combine like terms: -7.288617885 + 7.288617885 = 0.000000000 0.000000000 + x = 1.777217916 + 7.288617885 x = 1.777217916 + 7.288617885 Combine like terms: 1.777217916 + 7.288617885 = 9.065835801 x = 9.065835801 Simplifying x = 9.065835801Subproblem 2
x + -7.288617885 = -1.777217916 Simplifying x + -7.288617885 = -1.777217916 Reorder the terms: -7.288617885 + x = -1.777217916 Solving -7.288617885 + x = -1.777217916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.288617885' to each side of the equation. -7.288617885 + 7.288617885 + x = -1.777217916 + 7.288617885 Combine like terms: -7.288617885 + 7.288617885 = 0.000000000 0.000000000 + x = -1.777217916 + 7.288617885 x = -1.777217916 + 7.288617885 Combine like terms: -1.777217916 + 7.288617885 = 5.511399969 x = 5.511399969 Simplifying x = 5.511399969Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.065835801, 5.511399969}
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