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Simplifying (3x + -2)(3x + -2) = 15 Reorder the terms: (-2 + 3x)(3x + -2) = 15 Reorder the terms: (-2 + 3x)(-2 + 3x) = 15 Multiply (-2 + 3x) * (-2 + 3x) (-2(-2 + 3x) + 3x * (-2 + 3x)) = 15 ((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = 15 ((4 + -6x) + 3x * (-2 + 3x)) = 15 (4 + -6x + (-2 * 3x + 3x * 3x)) = 15 (4 + -6x + (-6x + 9x2)) = 15 Combine like terms: -6x + -6x = -12x (4 + -12x + 9x2) = 15 Solving 4 + -12x + 9x2 = 15 Solving for variable 'x'. Reorder the terms: 4 + -15 + -12x + 9x2 = 15 + -15 Combine like terms: 4 + -15 = -11 -11 + -12x + 9x2 = 15 + -15 Combine like terms: 15 + -15 = 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 = 1.9576611155 x = 1.9576611155 Simplifying x = 1.9576611155Subproblem 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 = -0.6243277825 x = -0.6243277825 Simplifying x = -0.6243277825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9576611155, -0.6243277825}
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