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Simplifying (6x + -2)(3x + 5) = 9 Reorder the terms: (-2 + 6x)(3x + 5) = 9 Reorder the terms: (-2 + 6x)(5 + 3x) = 9 Multiply (-2 + 6x) * (5 + 3x) (-2(5 + 3x) + 6x * (5 + 3x)) = 9 ((5 * -2 + 3x * -2) + 6x * (5 + 3x)) = 9 ((-10 + -6x) + 6x * (5 + 3x)) = 9 (-10 + -6x + (5 * 6x + 3x * 6x)) = 9 (-10 + -6x + (30x + 18x2)) = 9 Combine like terms: -6x + 30x = 24x (-10 + 24x + 18x2) = 9 Solving -10 + 24x + 18x2 = 9 Solving for variable 'x'. Reorder the terms: -10 + -9 + 24x + 18x2 = 9 + -9 Combine like terms: -10 + -9 = -19 -19 + 24x + 18x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -19 + 24x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.055555556 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1.055555556' to each side of the equation. -1.055555556 + 1.333333333x + 1.055555556 + x2 = 0 + 1.055555556 Reorder the terms: -1.055555556 + 1.055555556 + 1.333333333x + x2 = 0 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 1.055555556 1.333333333x + x2 = 0 + 1.055555556 Combine like terms: 0 + 1.055555556 = 1.055555556 1.333333333x + x2 = 1.055555556 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 = 1.055555556 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1.055555556 + 0.4444444442 Combine like terms: 1.055555556 + 0.4444444442 = 1.5000000002 0.4444444442 + 1.333333333x + x2 = 1.5000000002 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.5000000002 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 0.6666666665 = 1.224744871 Simplifying x + 0.6666666665 = 1.224744871 Reorder the terms: 0.6666666665 + x = 1.224744871 Solving 0.6666666665 + x = 1.224744871 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 = 1.224744871 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.224744871 + -0.6666666665 x = 1.224744871 + -0.6666666665 Combine like terms: 1.224744871 + -0.6666666665 = 0.5580782045 x = 0.5580782045 Simplifying x = 0.5580782045Subproblem 2
x + 0.6666666665 = -1.224744871 Simplifying x + 0.6666666665 = -1.224744871 Reorder the terms: 0.6666666665 + x = -1.224744871 Solving 0.6666666665 + x = -1.224744871 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 = -1.224744871 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.224744871 + -0.6666666665 x = -1.224744871 + -0.6666666665 Combine like terms: -1.224744871 + -0.6666666665 = -1.8914115375 x = -1.8914115375 Simplifying x = -1.8914115375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5580782045, -1.8914115375}
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