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Simplifying (3x + 7)(3x + 7) = 18 Reorder the terms: (7 + 3x)(3x + 7) = 18 Reorder the terms: (7 + 3x)(7 + 3x) = 18 Multiply (7 + 3x) * (7 + 3x) (7(7 + 3x) + 3x * (7 + 3x)) = 18 ((7 * 7 + 3x * 7) + 3x * (7 + 3x)) = 18 ((49 + 21x) + 3x * (7 + 3x)) = 18 (49 + 21x + (7 * 3x + 3x * 3x)) = 18 (49 + 21x + (21x + 9x2)) = 18 Combine like terms: 21x + 21x = 42x (49 + 42x + 9x2) = 18 Solving 49 + 42x + 9x2 = 18 Solving for variable 'x'. Reorder the terms: 49 + -18 + 42x + 9x2 = 18 + -18 Combine like terms: 49 + -18 = 31 31 + 42x + 9x2 = 18 + -18 Combine like terms: 18 + -18 = 0 31 + 42x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.444444444 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '-3.444444444' to each side of the equation. 3.444444444 + 4.666666667x + -3.444444444 + x2 = 0 + -3.444444444 Reorder the terms: 3.444444444 + -3.444444444 + 4.666666667x + x2 = 0 + -3.444444444 Combine like terms: 3.444444444 + -3.444444444 = 0.000000000 0.000000000 + 4.666666667x + x2 = 0 + -3.444444444 4.666666667x + x2 = 0 + -3.444444444 Combine like terms: 0 + -3.444444444 = -3.444444444 4.666666667x + x2 = -3.444444444 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = -3.444444444 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = -3.444444444 + 5.444444448 Combine like terms: -3.444444444 + 5.444444448 = 2.000000004 5.444444448 + 4.666666667x + x2 = 2.000000004 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 2.000000004 Calculate the square root of the right side: 1.414213564 Break this problem into two subproblems by setting (x + 2.333333334) equal to 1.414213564 and -1.414213564.Subproblem 1
x + 2.333333334 = 1.414213564 Simplifying x + 2.333333334 = 1.414213564 Reorder the terms: 2.333333334 + x = 1.414213564 Solving 2.333333334 + x = 1.414213564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 1.414213564 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 1.414213564 + -2.333333334 x = 1.414213564 + -2.333333334 Combine like terms: 1.414213564 + -2.333333334 = -0.91911977 x = -0.91911977 Simplifying x = -0.91911977Subproblem 2
x + 2.333333334 = -1.414213564 Simplifying x + 2.333333334 = -1.414213564 Reorder the terms: 2.333333334 + x = -1.414213564 Solving 2.333333334 + x = -1.414213564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -1.414213564 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -1.414213564 + -2.333333334 x = -1.414213564 + -2.333333334 Combine like terms: -1.414213564 + -2.333333334 = -3.747546898 x = -3.747546898 Simplifying x = -3.747546898Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.91911977, -3.747546898}
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