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Simplifying (3x + -1)(3x + 2) = 2x Reorder the terms: (-1 + 3x)(3x + 2) = 2x Reorder the terms: (-1 + 3x)(2 + 3x) = 2x Multiply (-1 + 3x) * (2 + 3x) (-1(2 + 3x) + 3x * (2 + 3x)) = 2x ((2 * -1 + 3x * -1) + 3x * (2 + 3x)) = 2x ((-2 + -3x) + 3x * (2 + 3x)) = 2x (-2 + -3x + (2 * 3x + 3x * 3x)) = 2x (-2 + -3x + (6x + 9x2)) = 2x Combine like terms: -3x + 6x = 3x (-2 + 3x + 9x2) = 2x Solving -2 + 3x + 9x2 = 2x Solving for variable 'x'. Reorder the terms: -2 + 3x + -2x + 9x2 = 2x + -2x Combine like terms: 3x + -2x = 1x -2 + 1x + 9x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -2 + 1x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.1111111111x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.1111111111x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + 0.2222222222 0.1111111111x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.1111111111x + x2 = 0.2222222222 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = 0.2222222222 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.2222222222 + 0.003086419752 Combine like terms: 0.2222222222 + 0.003086419752 = 0.225308641952 0.003086419752 + 0.1111111111x + x2 = 0.225308641952 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.225308641952 Calculate the square root of the right side: 0.474666875 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.474666875 and -0.474666875.Subproblem 1
x + 0.05555555555 = 0.474666875 Simplifying x + 0.05555555555 = 0.474666875 Reorder the terms: 0.05555555555 + x = 0.474666875 Solving 0.05555555555 + x = 0.474666875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 0.474666875 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.474666875 + -0.05555555555 x = 0.474666875 + -0.05555555555 Combine like terms: 0.474666875 + -0.05555555555 = 0.41911131945 x = 0.41911131945 Simplifying x = 0.41911131945Subproblem 2
x + 0.05555555555 = -0.474666875 Simplifying x + 0.05555555555 = -0.474666875 Reorder the terms: 0.05555555555 + x = -0.474666875 Solving 0.05555555555 + x = -0.474666875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -0.474666875 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.474666875 + -0.05555555555 x = -0.474666875 + -0.05555555555 Combine like terms: -0.474666875 + -0.05555555555 = -0.53022243055 x = -0.53022243055 Simplifying x = -0.53022243055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41911131945, -0.53022243055}
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