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Simplifying (3x + 4)(3x + 4) = 14 Reorder the terms: (4 + 3x)(3x + 4) = 14 Reorder the terms: (4 + 3x)(4 + 3x) = 14 Multiply (4 + 3x) * (4 + 3x) (4(4 + 3x) + 3x * (4 + 3x)) = 14 ((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 14 ((16 + 12x) + 3x * (4 + 3x)) = 14 (16 + 12x + (4 * 3x + 3x * 3x)) = 14 (16 + 12x + (12x + 9x2)) = 14 Combine like terms: 12x + 12x = 24x (16 + 24x + 9x2) = 14 Solving 16 + 24x + 9x2 = 14 Solving for variable 'x'. Reorder the terms: 16 + -14 + 24x + 9x2 = 14 + -14 Combine like terms: 16 + -14 = 2 2 + 24x + 9x2 = 14 + -14 Combine like terms: 14 + -14 = 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 = 1.5555555578 1.777777780 + 2.666666667x + x2 = 1.5555555578 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 1.5555555578 Calculate the square root of the right side: 1.24721913 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.24721913 and -1.24721913.Subproblem 1
x + 1.333333334 = 1.24721913 Simplifying x + 1.333333334 = 1.24721913 Reorder the terms: 1.333333334 + x = 1.24721913 Solving 1.333333334 + x = 1.24721913 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 = 1.24721913 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.24721913 + -1.333333334 x = 1.24721913 + -1.333333334 Combine like terms: 1.24721913 + -1.333333334 = -0.086114204 x = -0.086114204 Simplifying x = -0.086114204Subproblem 2
x + 1.333333334 = -1.24721913 Simplifying x + 1.333333334 = -1.24721913 Reorder the terms: 1.333333334 + x = -1.24721913 Solving 1.333333334 + x = -1.24721913 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 = -1.24721913 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.24721913 + -1.333333334 x = -1.24721913 + -1.333333334 Combine like terms: -1.24721913 + -1.333333334 = -2.580552464 x = -2.580552464 Simplifying x = -2.580552464Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.086114204, -2.580552464}
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