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Simplifying 4.56x2 + -9.64x + 4.13 = 0 Reorder the terms: 4.13 + -9.64x + 4.56x2 = 0 Solving 4.13 + -9.64x + 4.56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.56 the coefficient of the squared term: Divide each side by '4.56'. 0.9057017544 + -2.114035088x + x2 = 0 Move the constant term to the right: Add '-0.9057017544' to each side of the equation. 0.9057017544 + -2.114035088x + -0.9057017544 + x2 = 0 + -0.9057017544 Reorder the terms: 0.9057017544 + -0.9057017544 + -2.114035088x + x2 = 0 + -0.9057017544 Combine like terms: 0.9057017544 + -0.9057017544 = 0.0000000000 0.0000000000 + -2.114035088x + x2 = 0 + -0.9057017544 -2.114035088x + x2 = 0 + -0.9057017544 Combine like terms: 0 + -0.9057017544 = -0.9057017544 -2.114035088x + x2 = -0.9057017544 The x term is -2.114035088x. Take half its coefficient (-1.057017544). Square it (1.117286088) and add it to both sides. Add '1.117286088' to each side of the equation. -2.114035088x + 1.117286088 + x2 = -0.9057017544 + 1.117286088 Reorder the terms: 1.117286088 + -2.114035088x + x2 = -0.9057017544 + 1.117286088 Combine like terms: -0.9057017544 + 1.117286088 = 0.2115843336 1.117286088 + -2.114035088x + x2 = 0.2115843336 Factor a perfect square on the left side: (x + -1.057017544)(x + -1.057017544) = 0.2115843336 Calculate the square root of the right side: 0.459982971 Break this problem into two subproblems by setting (x + -1.057017544) equal to 0.459982971 and -0.459982971.Subproblem 1
x + -1.057017544 = 0.459982971 Simplifying x + -1.057017544 = 0.459982971 Reorder the terms: -1.057017544 + x = 0.459982971 Solving -1.057017544 + x = 0.459982971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.057017544' to each side of the equation. -1.057017544 + 1.057017544 + x = 0.459982971 + 1.057017544 Combine like terms: -1.057017544 + 1.057017544 = 0.000000000 0.000000000 + x = 0.459982971 + 1.057017544 x = 0.459982971 + 1.057017544 Combine like terms: 0.459982971 + 1.057017544 = 1.517000515 x = 1.517000515 Simplifying x = 1.517000515Subproblem 2
x + -1.057017544 = -0.459982971 Simplifying x + -1.057017544 = -0.459982971 Reorder the terms: -1.057017544 + x = -0.459982971 Solving -1.057017544 + x = -0.459982971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.057017544' to each side of the equation. -1.057017544 + 1.057017544 + x = -0.459982971 + 1.057017544 Combine like terms: -1.057017544 + 1.057017544 = 0.000000000 0.000000000 + x = -0.459982971 + 1.057017544 x = -0.459982971 + 1.057017544 Combine like terms: -0.459982971 + 1.057017544 = 0.597034573 x = 0.597034573 Simplifying x = 0.597034573Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.517000515, 0.597034573}
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