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Simplifying (3x + 2)(x + 1) = 3x + 17 Reorder the terms: (2 + 3x)(x + 1) = 3x + 17 Reorder the terms: (2 + 3x)(1 + x) = 3x + 17 Multiply (2 + 3x) * (1 + x) (2(1 + x) + 3x * (1 + x)) = 3x + 17 ((1 * 2 + x * 2) + 3x * (1 + x)) = 3x + 17 ((2 + 2x) + 3x * (1 + x)) = 3x + 17 (2 + 2x + (1 * 3x + x * 3x)) = 3x + 17 (2 + 2x + (3x + 3x2)) = 3x + 17 Combine like terms: 2x + 3x = 5x (2 + 5x + 3x2) = 3x + 17 Reorder the terms: 2 + 5x + 3x2 = 17 + 3x Solving 2 + 5x + 3x2 = 17 + 3x Solving for variable 'x'. Reorder the terms: 2 + -17 + 5x + -3x + 3x2 = 17 + 3x + -17 + -3x Combine like terms: 2 + -17 = -15 -15 + 5x + -3x + 3x2 = 17 + 3x + -17 + -3x Combine like terms: 5x + -3x = 2x -15 + 2x + 3x2 = 17 + 3x + -17 + -3x Reorder the terms: -15 + 2x + 3x2 = 17 + -17 + 3x + -3x Combine like terms: 17 + -17 = 0 -15 + 2x + 3x2 = 0 + 3x + -3x -15 + 2x + 3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -15 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.6666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.6666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.6666666667x + x2 = 0 + 5 0.6666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.6666666667x + x2 = 5 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 5 + 0.1111111112 Combine like terms: 5 + 0.1111111112 = 5.1111111112 0.1111111112 + 0.6666666667x + x2 = 5.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 5.1111111112 Calculate the square root of the right side: 2.260776661 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 2.260776661 and -2.260776661.Subproblem 1
x + 0.3333333334 = 2.260776661 Simplifying x + 0.3333333334 = 2.260776661 Reorder the terms: 0.3333333334 + x = 2.260776661 Solving 0.3333333334 + x = 2.260776661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 2.260776661 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 2.260776661 + -0.3333333334 x = 2.260776661 + -0.3333333334 Combine like terms: 2.260776661 + -0.3333333334 = 1.9274433276 x = 1.9274433276 Simplifying x = 1.9274433276Subproblem 2
x + 0.3333333334 = -2.260776661 Simplifying x + 0.3333333334 = -2.260776661 Reorder the terms: 0.3333333334 + x = -2.260776661 Solving 0.3333333334 + x = -2.260776661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -2.260776661 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -2.260776661 + -0.3333333334 x = -2.260776661 + -0.3333333334 Combine like terms: -2.260776661 + -0.3333333334 = -2.5941099944 x = -2.5941099944 Simplifying x = -2.5941099944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9274433276, -2.5941099944}
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