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Simplifying (6x + -1)(2x + 3) = 5x Reorder the terms: (-1 + 6x)(2x + 3) = 5x Reorder the terms: (-1 + 6x)(3 + 2x) = 5x Multiply (-1 + 6x) * (3 + 2x) (-1(3 + 2x) + 6x * (3 + 2x)) = 5x ((3 * -1 + 2x * -1) + 6x * (3 + 2x)) = 5x ((-3 + -2x) + 6x * (3 + 2x)) = 5x (-3 + -2x + (3 * 6x + 2x * 6x)) = 5x (-3 + -2x + (18x + 12x2)) = 5x Combine like terms: -2x + 18x = 16x (-3 + 16x + 12x2) = 5x Solving -3 + 16x + 12x2 = 5x Solving for variable 'x'. Reorder the terms: -3 + 16x + -5x + 12x2 = 5x + -5x Combine like terms: 16x + -5x = 11x -3 + 11x + 12x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -3 + 11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.25 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.9166666667x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.9166666667x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.9166666667x + x2 = 0 + 0.25 0.9166666667x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.9166666667x + x2 = 0.25 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 0.25 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.25 + 0.2100694445 Combine like terms: 0.25 + 0.2100694445 = 0.4600694445 0.2100694445 + 0.9166666667x + x2 = 0.4600694445 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 0.4600694445 Calculate the square root of the right side: 0.678284192 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 0.678284192 and -0.678284192.Subproblem 1
x + 0.4583333334 = 0.678284192 Simplifying x + 0.4583333334 = 0.678284192 Reorder the terms: 0.4583333334 + x = 0.678284192 Solving 0.4583333334 + x = 0.678284192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 0.678284192 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 0.678284192 + -0.4583333334 x = 0.678284192 + -0.4583333334 Combine like terms: 0.678284192 + -0.4583333334 = 0.2199508586 x = 0.2199508586 Simplifying x = 0.2199508586Subproblem 2
x + 0.4583333334 = -0.678284192 Simplifying x + 0.4583333334 = -0.678284192 Reorder the terms: 0.4583333334 + x = -0.678284192 Solving 0.4583333334 + x = -0.678284192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -0.678284192 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -0.678284192 + -0.4583333334 x = -0.678284192 + -0.4583333334 Combine like terms: -0.678284192 + -0.4583333334 = -1.1366175254 x = -1.1366175254 Simplifying x = -1.1366175254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2199508586, -1.1366175254}
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