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Simplifying (3x + 2)(3x + 2) + -8 = 7 Reorder the terms: (2 + 3x)(3x + 2) + -8 = 7 Reorder the terms: (2 + 3x)(2 + 3x) + -8 = 7 Multiply (2 + 3x) * (2 + 3x) (2(2 + 3x) + 3x * (2 + 3x)) + -8 = 7 ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + -8 = 7 ((4 + 6x) + 3x * (2 + 3x)) + -8 = 7 (4 + 6x + (2 * 3x + 3x * 3x)) + -8 = 7 (4 + 6x + (6x + 9x2)) + -8 = 7 Combine like terms: 6x + 6x = 12x (4 + 12x + 9x2) + -8 = 7 Reorder the terms: 4 + -8 + 12x + 9x2 = 7 Combine like terms: 4 + -8 = -4 -4 + 12x + 9x2 = 7 Solving -4 + 12x + 9x2 = 7 Solving for variable 'x'. Reorder the terms: -4 + -7 + 12x + 9x2 = 7 + -7 Combine like terms: -4 + -7 = -11 -11 + 12x + 9x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -11 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 1.333333333x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 1.333333333x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 1.222222222 1.333333333x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 1.333333333x + x2 = 1.222222222 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 1.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1.222222222 + 0.4444444442 Combine like terms: 1.222222222 + 0.4444444442 = 1.6666666662 0.4444444442 + 1.333333333x + x2 = 1.6666666662 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.6666666662 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.290994449 and -1.290994449.Subproblem 1
x + 0.6666666665 = 1.290994449 Simplifying x + 0.6666666665 = 1.290994449 Reorder the terms: 0.6666666665 + x = 1.290994449 Solving 0.6666666665 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.290994449 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.290994449 + -0.6666666665 x = 1.290994449 + -0.6666666665 Combine like terms: 1.290994449 + -0.6666666665 = 0.6243277825 x = 0.6243277825 Simplifying x = 0.6243277825Subproblem 2
x + 0.6666666665 = -1.290994449 Simplifying x + 0.6666666665 = -1.290994449 Reorder the terms: 0.6666666665 + x = -1.290994449 Solving 0.6666666665 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.290994449 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.290994449 + -0.6666666665 x = -1.290994449 + -0.6666666665 Combine like terms: -1.290994449 + -0.6666666665 = -1.9576611155 x = -1.9576611155 Simplifying x = -1.9576611155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6243277825, -1.9576611155}
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