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Simplifying (4x + -2)(3x + -4) = 9 Reorder the terms: (-2 + 4x)(3x + -4) = 9 Reorder the terms: (-2 + 4x)(-4 + 3x) = 9 Multiply (-2 + 4x) * (-4 + 3x) (-2(-4 + 3x) + 4x * (-4 + 3x)) = 9 ((-4 * -2 + 3x * -2) + 4x * (-4 + 3x)) = 9 ((8 + -6x) + 4x * (-4 + 3x)) = 9 (8 + -6x + (-4 * 4x + 3x * 4x)) = 9 (8 + -6x + (-16x + 12x2)) = 9 Combine like terms: -6x + -16x = -22x (8 + -22x + 12x2) = 9 Solving 8 + -22x + 12x2 = 9 Solving for variable 'x'. Reorder the terms: 8 + -9 + -22x + 12x2 = 9 + -9 Combine like terms: 8 + -9 = -1 -1 + -22x + 12x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -1 + -22x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + -1.833333333x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -1.833333333x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -1.833333333x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -1.833333333x + x2 = 0 + 0.08333333333 -1.833333333x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -1.833333333x + x2 = 0.08333333333 The x term is -1.833333333x. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333x + 0.8402777775 + x2 = 0.08333333333 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333x + x2 = 0.08333333333 + 0.8402777775 Combine like terms: 0.08333333333 + 0.8402777775 = 0.92361111083 0.8402777775 + -1.833333333x + x2 = 0.92361111083 Factor a perfect square on the left side: (x + -0.9166666665)(x + -0.9166666665) = 0.92361111083 Calculate the square root of the right side: 0.961046883 Break this problem into two subproblems by setting (x + -0.9166666665) equal to 0.961046883 and -0.961046883.Subproblem 1
x + -0.9166666665 = 0.961046883 Simplifying x + -0.9166666665 = 0.961046883 Reorder the terms: -0.9166666665 + x = 0.961046883 Solving -0.9166666665 + x = 0.961046883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = 0.961046883 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = 0.961046883 + 0.9166666665 x = 0.961046883 + 0.9166666665 Combine like terms: 0.961046883 + 0.9166666665 = 1.8777135495 x = 1.8777135495 Simplifying x = 1.8777135495Subproblem 2
x + -0.9166666665 = -0.961046883 Simplifying x + -0.9166666665 = -0.961046883 Reorder the terms: -0.9166666665 + x = -0.961046883 Solving -0.9166666665 + x = -0.961046883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + x = -0.961046883 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + x = -0.961046883 + 0.9166666665 x = -0.961046883 + 0.9166666665 Combine like terms: -0.961046883 + 0.9166666665 = -0.0443802165 x = -0.0443802165 Simplifying x = -0.0443802165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8777135495, -0.0443802165}
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