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Simplifying (5x + -1)(2x + 3) = 4x Reorder the terms: (-1 + 5x)(2x + 3) = 4x Reorder the terms: (-1 + 5x)(3 + 2x) = 4x Multiply (-1 + 5x) * (3 + 2x) (-1(3 + 2x) + 5x * (3 + 2x)) = 4x ((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 4x ((-3 + -2x) + 5x * (3 + 2x)) = 4x (-3 + -2x + (3 * 5x + 2x * 5x)) = 4x (-3 + -2x + (15x + 10x2)) = 4x Combine like terms: -2x + 15x = 13x (-3 + 13x + 10x2) = 4x Solving -3 + 13x + 10x2 = 4x Solving for variable 'x'. Reorder the terms: -3 + 13x + -4x + 10x2 = 4x + -4x Combine like terms: 13x + -4x = 9x -3 + 9x + 10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -3 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.9x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.9x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.9x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.9x + x2 = 0.0 + 0.3 0.9x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.9x + x2 = 0.3 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 0.3 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 0.3 + 0.2025 Combine like terms: 0.3 + 0.2025 = 0.5025 0.2025 + 0.9x + x2 = 0.5025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + 0.45) equal to 0.708872344 and -0.708872344.Subproblem 1
x + 0.45 = 0.708872344 Simplifying x + 0.45 = 0.708872344 Reorder the terms: 0.45 + x = 0.708872344 Solving 0.45 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.708872344 + -0.45 x = 0.708872344 + -0.45 Combine like terms: 0.708872344 + -0.45 = 0.258872344 x = 0.258872344 Simplifying x = 0.258872344Subproblem 2
x + 0.45 = -0.708872344 Simplifying x + 0.45 = -0.708872344 Reorder the terms: 0.45 + x = -0.708872344 Solving 0.45 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -0.708872344 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.708872344 + -0.45 x = -0.708872344 + -0.45 Combine like terms: -0.708872344 + -0.45 = -1.158872344 x = -1.158872344 Simplifying x = -1.158872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.258872344, -1.158872344}
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