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Simplifying (3x + 4)(3x + 4) = 18 Reorder the terms: (4 + 3x)(3x + 4) = 18 Reorder the terms: (4 + 3x)(4 + 3x) = 18 Multiply (4 + 3x) * (4 + 3x) (4(4 + 3x) + 3x * (4 + 3x)) = 18 ((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 18 ((16 + 12x) + 3x * (4 + 3x)) = 18 (16 + 12x + (4 * 3x + 3x * 3x)) = 18 (16 + 12x + (12x + 9x2)) = 18 Combine like terms: 12x + 12x = 24x (16 + 24x + 9x2) = 18 Solving 16 + 24x + 9x2 = 18 Solving for variable 'x'. Reorder the terms: 16 + -18 + 24x + 9x2 = 18 + -18 Combine like terms: 16 + -18 = -2 -2 + 24x + 9x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -2 + 24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 2.666666667x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 2.666666667x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + 0.2222222222 2.666666667x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 2.666666667x + x2 = 0.2222222222 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 0.2222222222 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 0.2222222222 + 1.777777780 Combine like terms: 0.2222222222 + 1.777777780 = 2.0000000022 1.777777780 + 2.666666667x + x2 = 2.0000000022 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.0000000022 Calculate the square root of the right side: 1.414213563 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.414213563 and -1.414213563.Subproblem 1
x + 1.333333334 = 1.414213563 Simplifying x + 1.333333334 = 1.414213563 Reorder the terms: 1.333333334 + x = 1.414213563 Solving 1.333333334 + x = 1.414213563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.414213563 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.414213563 + -1.333333334 x = 1.414213563 + -1.333333334 Combine like terms: 1.414213563 + -1.333333334 = 0.080880229 x = 0.080880229 Simplifying x = 0.080880229Subproblem 2
x + 1.333333334 = -1.414213563 Simplifying x + 1.333333334 = -1.414213563 Reorder the terms: 1.333333334 + x = -1.414213563 Solving 1.333333334 + x = -1.414213563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.414213563 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.414213563 + -1.333333334 x = -1.414213563 + -1.333333334 Combine like terms: -1.414213563 + -1.333333334 = -2.747546897 x = -2.747546897 Simplifying x = -2.747546897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.080880229, -2.747546897}
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