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Simplifying (3x + -1)(x + 2) = -1 Reorder the terms: (-1 + 3x)(x + 2) = -1 Reorder the terms: (-1 + 3x)(2 + x) = -1 Multiply (-1 + 3x) * (2 + x) (-1(2 + x) + 3x * (2 + x)) = -1 ((2 * -1 + x * -1) + 3x * (2 + x)) = -1 ((-2 + -1x) + 3x * (2 + x)) = -1 (-2 + -1x + (2 * 3x + x * 3x)) = -1 (-2 + -1x + (6x + 3x2)) = -1 Combine like terms: -1x + 6x = 5x (-2 + 5x + 3x2) = -1 Solving -2 + 5x + 3x2 = -1 Solving for variable 'x'. Reorder the terms: -2 + 1 + 5x + 3x2 = -1 + 1 Combine like terms: -2 + 1 = -1 -1 + 5x + 3x2 = -1 + 1 Combine like terms: -1 + 1 = 0 -1 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.666666667x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.3333333333 1.666666667x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.666666667x + x2 = 0.3333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.3333333333 + 0.6944444447 Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778 0.6944444447 + 1.666666667x + x2 = 1.027777778 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.013793755 and -1.013793755.Subproblem 1
x + 0.8333333335 = 1.013793755 Simplifying x + 0.8333333335 = 1.013793755 Reorder the terms: 0.8333333335 + x = 1.013793755 Solving 0.8333333335 + x = 1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.013793755 + -0.8333333335 x = 1.013793755 + -0.8333333335 Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215 x = 0.1804604215 Simplifying x = 0.1804604215Subproblem 2
x + 0.8333333335 = -1.013793755 Simplifying x + 0.8333333335 = -1.013793755 Reorder the terms: 0.8333333335 + x = -1.013793755 Solving 0.8333333335 + x = -1.013793755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.013793755 + -0.8333333335 x = -1.013793755 + -0.8333333335 Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885 x = -1.8471270885 Simplifying x = -1.8471270885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1804604215, -1.8471270885}
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