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Simplifying (3x + -1)(x + 2) = 42 Reorder the terms: (-1 + 3x)(x + 2) = 42 Reorder the terms: (-1 + 3x)(2 + x) = 42 Multiply (-1 + 3x) * (2 + x) (-1(2 + x) + 3x * (2 + x)) = 42 ((2 * -1 + x * -1) + 3x * (2 + x)) = 42 ((-2 + -1x) + 3x * (2 + x)) = 42 (-2 + -1x + (2 * 3x + x * 3x)) = 42 (-2 + -1x + (6x + 3x2)) = 42 Combine like terms: -1x + 6x = 5x (-2 + 5x + 3x2) = 42 Solving -2 + 5x + 3x2 = 42 Solving for variable 'x'. Reorder the terms: -2 + -42 + 5x + 3x2 = 42 + -42 Combine like terms: -2 + -42 = -44 -44 + 5x + 3x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -44 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + 1.666666667x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + 1.666666667x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + 1.666666667x + x2 = 0 + 14.66666667 1.666666667x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 1.666666667x + x2 = 14.66666667 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 = 14.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 14.66666667 + 0.6944444447 Combine like terms: 14.66666667 + 0.6944444447 = 15.3611111147 0.6944444447 + 1.666666667x + x2 = 15.3611111147 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 15.3611111147 Calculate the square root of the right side: 3.919325339 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.919325339 and -3.919325339.Subproblem 1
x + 0.8333333335 = 3.919325339 Simplifying x + 0.8333333335 = 3.919325339 Reorder the terms: 0.8333333335 + x = 3.919325339 Solving 0.8333333335 + x = 3.919325339 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 = 3.919325339 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.919325339 + -0.8333333335 x = 3.919325339 + -0.8333333335 Combine like terms: 3.919325339 + -0.8333333335 = 3.0859920055 x = 3.0859920055 Simplifying x = 3.0859920055Subproblem 2
x + 0.8333333335 = -3.919325339 Simplifying x + 0.8333333335 = -3.919325339 Reorder the terms: 0.8333333335 + x = -3.919325339 Solving 0.8333333335 + x = -3.919325339 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 = -3.919325339 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.919325339 + -0.8333333335 x = -3.919325339 + -0.8333333335 Combine like terms: -3.919325339 + -0.8333333335 = -4.7526586725 x = -4.7526586725 Simplifying x = -4.7526586725Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0859920055, -4.7526586725}
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