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Simplifying 422x2 + -506x + -347 = 0 Reorder the terms: -347 + -506x + 422x2 = 0 Solving -347 + -506x + 422x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 422 the coefficient of the squared term: Divide each side by '422'. -0.8222748815 + -1.199052133x + x2 = 0 Move the constant term to the right: Add '0.8222748815' to each side of the equation. -0.8222748815 + -1.199052133x + 0.8222748815 + x2 = 0 + 0.8222748815 Reorder the terms: -0.8222748815 + 0.8222748815 + -1.199052133x + x2 = 0 + 0.8222748815 Combine like terms: -0.8222748815 + 0.8222748815 = 0.0000000000 0.0000000000 + -1.199052133x + x2 = 0 + 0.8222748815 -1.199052133x + x2 = 0 + 0.8222748815 Combine like terms: 0 + 0.8222748815 = 0.8222748815 -1.199052133x + x2 = 0.8222748815 The x term is -1.199052133x. Take half its coefficient (-0.5995260665). Square it (0.3594315044) and add it to both sides. Add '0.3594315044' to each side of the equation. -1.199052133x + 0.3594315044 + x2 = 0.8222748815 + 0.3594315044 Reorder the terms: 0.3594315044 + -1.199052133x + x2 = 0.8222748815 + 0.3594315044 Combine like terms: 0.8222748815 + 0.3594315044 = 1.1817063859 0.3594315044 + -1.199052133x + x2 = 1.1817063859 Factor a perfect square on the left side: (x + -0.5995260665)(x + -0.5995260665) = 1.1817063859 Calculate the square root of the right side: 1.087063193 Break this problem into two subproblems by setting (x + -0.5995260665) equal to 1.087063193 and -1.087063193.Subproblem 1
x + -0.5995260665 = 1.087063193 Simplifying x + -0.5995260665 = 1.087063193 Reorder the terms: -0.5995260665 + x = 1.087063193 Solving -0.5995260665 + x = 1.087063193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5995260665' to each side of the equation. -0.5995260665 + 0.5995260665 + x = 1.087063193 + 0.5995260665 Combine like terms: -0.5995260665 + 0.5995260665 = 0.0000000000 0.0000000000 + x = 1.087063193 + 0.5995260665 x = 1.087063193 + 0.5995260665 Combine like terms: 1.087063193 + 0.5995260665 = 1.6865892595 x = 1.6865892595 Simplifying x = 1.6865892595Subproblem 2
x + -0.5995260665 = -1.087063193 Simplifying x + -0.5995260665 = -1.087063193 Reorder the terms: -0.5995260665 + x = -1.087063193 Solving -0.5995260665 + x = -1.087063193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5995260665' to each side of the equation. -0.5995260665 + 0.5995260665 + x = -1.087063193 + 0.5995260665 Combine like terms: -0.5995260665 + 0.5995260665 = 0.0000000000 0.0000000000 + x = -1.087063193 + 0.5995260665 x = -1.087063193 + 0.5995260665 Combine like terms: -1.087063193 + 0.5995260665 = -0.4875371265 x = -0.4875371265 Simplifying x = -0.4875371265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6865892595, -0.4875371265}
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