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Simplifying (x + 1)(3x + -2) + -2x + -4 = 0 Reorder the terms: (1 + x)(3x + -2) + -2x + -4 = 0 Reorder the terms: (1 + x)(-2 + 3x) + -2x + -4 = 0 Multiply (1 + x) * (-2 + 3x) (1(-2 + 3x) + x(-2 + 3x)) + -2x + -4 = 0 ((-2 * 1 + 3x * 1) + x(-2 + 3x)) + -2x + -4 = 0 ((-2 + 3x) + x(-2 + 3x)) + -2x + -4 = 0 (-2 + 3x + (-2 * x + 3x * x)) + -2x + -4 = 0 (-2 + 3x + (-2x + 3x2)) + -2x + -4 = 0 Combine like terms: 3x + -2x = 1x (-2 + 1x + 3x2) + -2x + -4 = 0 Reorder the terms: -2 + -4 + 1x + -2x + 3x2 = 0 Combine like terms: -2 + -4 = -6 -6 + 1x + -2x + 3x2 = 0 Combine like terms: 1x + -2x = -1x -6 + -1x + 3x2 = 0 Solving -6 + -1x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.3333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.3333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.3333333333x + x2 = 0 + 2 -0.3333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.3333333333x + x2 = 2 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 2 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 2 + 0.02777777779 Combine like terms: 2 + 0.02777777779 = 2.02777777779 0.02777777779 + -0.3333333333x + x2 = 2.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 2.02777777779 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.424000624 and -1.424000624.Subproblem 1
x + -0.1666666667 = 1.424000624 Simplifying x + -0.1666666667 = 1.424000624 Reorder the terms: -0.1666666667 + x = 1.424000624 Solving -0.1666666667 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.424000624 + 0.1666666667 x = 1.424000624 + 0.1666666667 Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907 x = 1.5906672907 Simplifying x = 1.5906672907Subproblem 2
x + -0.1666666667 = -1.424000624 Simplifying x + -0.1666666667 = -1.424000624 Reorder the terms: -0.1666666667 + x = -1.424000624 Solving -0.1666666667 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.424000624 + 0.1666666667 x = -1.424000624 + 0.1666666667 Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573 x = -1.2573339573 Simplifying x = -1.2573339573Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5906672907, -1.2573339573}
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