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Simplifying (3x + 2)(x + 1) = 3x * 2 + 17 Reorder the terms: (2 + 3x)(x + 1) = 3x * 2 + 17 Reorder the terms: (2 + 3x)(1 + x) = 3x * 2 + 17 Multiply (2 + 3x) * (1 + x) (2(1 + x) + 3x * (1 + x)) = 3x * 2 + 17 ((1 * 2 + x * 2) + 3x * (1 + x)) = 3x * 2 + 17 ((2 + 2x) + 3x * (1 + x)) = 3x * 2 + 17 (2 + 2x + (1 * 3x + x * 3x)) = 3x * 2 + 17 (2 + 2x + (3x + 3x2)) = 3x * 2 + 17 Combine like terms: 2x + 3x = 5x (2 + 5x + 3x2) = 3x * 2 + 17 Reorder the terms for easier multiplication: 2 + 5x + 3x2 = 3 * 2x + 17 Multiply 3 * 2 2 + 5x + 3x2 = 6x + 17 Reorder the terms: 2 + 5x + 3x2 = 17 + 6x Solving 2 + 5x + 3x2 = 17 + 6x Solving for variable 'x'. Reorder the terms: 2 + -17 + 5x + -6x + 3x2 = 17 + 6x + -17 + -6x Combine like terms: 2 + -17 = -15 -15 + 5x + -6x + 3x2 = 17 + 6x + -17 + -6x Combine like terms: 5x + -6x = -1x -15 + -1x + 3x2 = 17 + 6x + -17 + -6x Reorder the terms: -15 + -1x + 3x2 = 17 + -17 + 6x + -6x Combine like terms: 17 + -17 = 0 -15 + -1x + 3x2 = 0 + 6x + -6x -15 + -1x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -15 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.3333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.3333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.3333333333x + x2 = 0 + 5 -0.3333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.3333333333x + x2 = 5 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 = 5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 5 + 0.02777777779 Combine like terms: 5 + 0.02777777779 = 5.02777777779 0.02777777779 + -0.3333333333x + x2 = 5.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 5.02777777779 Calculate the square root of the right side: 2.242270675 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 2.242270675 and -2.242270675.Subproblem 1
x + -0.1666666667 = 2.242270675 Simplifying x + -0.1666666667 = 2.242270675 Reorder the terms: -0.1666666667 + x = 2.242270675 Solving -0.1666666667 + x = 2.242270675 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 = 2.242270675 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.242270675 + 0.1666666667 x = 2.242270675 + 0.1666666667 Combine like terms: 2.242270675 + 0.1666666667 = 2.4089373417 x = 2.4089373417 Simplifying x = 2.4089373417Subproblem 2
x + -0.1666666667 = -2.242270675 Simplifying x + -0.1666666667 = -2.242270675 Reorder the terms: -0.1666666667 + x = -2.242270675 Solving -0.1666666667 + x = -2.242270675 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 = -2.242270675 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.242270675 + 0.1666666667 x = -2.242270675 + 0.1666666667 Combine like terms: -2.242270675 + 0.1666666667 = -2.0756040083 x = -2.0756040083 Simplifying x = -2.0756040083Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4089373417, -2.0756040083}
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