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Simplifying (4x + -1)(2x + 4) = 3x Reorder the terms: (-1 + 4x)(2x + 4) = 3x Reorder the terms: (-1 + 4x)(4 + 2x) = 3x Multiply (-1 + 4x) * (4 + 2x) (-1(4 + 2x) + 4x * (4 + 2x)) = 3x ((4 * -1 + 2x * -1) + 4x * (4 + 2x)) = 3x ((-4 + -2x) + 4x * (4 + 2x)) = 3x (-4 + -2x + (4 * 4x + 2x * 4x)) = 3x (-4 + -2x + (16x + 8x2)) = 3x Combine like terms: -2x + 16x = 14x (-4 + 14x + 8x2) = 3x Solving -4 + 14x + 8x2 = 3x Solving for variable 'x'. Reorder the terms: -4 + 14x + -3x + 8x2 = 3x + -3x Combine like terms: 14x + -3x = 11x -4 + 11x + 8x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + 11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + 1.375x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.375x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.375x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.375x + x2 = 0 + 0.5 1.375x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.375x + x2 = 0.5 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 0.5 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 0.5 + 0.47265625 Combine like terms: 0.5 + 0.47265625 = 0.97265625 0.47265625 + 1.375x + x2 = 0.97265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (x + 0.6875) equal to 0.986233365 and -0.986233365.Subproblem 1
x + 0.6875 = 0.986233365 Simplifying x + 0.6875 = 0.986233365 Reorder the terms: 0.6875 + x = 0.986233365 Solving 0.6875 + x = 0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 0.986233365 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 0.986233365 + -0.6875 x = 0.986233365 + -0.6875 Combine like terms: 0.986233365 + -0.6875 = 0.298733365 x = 0.298733365 Simplifying x = 0.298733365Subproblem 2
x + 0.6875 = -0.986233365 Simplifying x + 0.6875 = -0.986233365 Reorder the terms: 0.6875 + x = -0.986233365 Solving 0.6875 + x = -0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -0.986233365 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -0.986233365 + -0.6875 x = -0.986233365 + -0.6875 Combine like terms: -0.986233365 + -0.6875 = -1.673733365 x = -1.673733365 Simplifying x = -1.673733365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.298733365, -1.673733365}
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