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Simplifying (4x + -1)(2x + 4) = 5x Reorder the terms: (-1 + 4x)(2x + 4) = 5x Reorder the terms: (-1 + 4x)(4 + 2x) = 5x Multiply (-1 + 4x) * (4 + 2x) (-1(4 + 2x) + 4x * (4 + 2x)) = 5x ((4 * -1 + 2x * -1) + 4x * (4 + 2x)) = 5x ((-4 + -2x) + 4x * (4 + 2x)) = 5x (-4 + -2x + (4 * 4x + 2x * 4x)) = 5x (-4 + -2x + (16x + 8x2)) = 5x Combine like terms: -2x + 16x = 14x (-4 + 14x + 8x2) = 5x Solving -4 + 14x + 8x2 = 5x Solving for variable 'x'. Reorder the terms: -4 + 14x + -5x + 8x2 = 5x + -5x Combine like terms: 14x + -5x = 9x -4 + 9x + 8x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -4 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.125x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.125x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.125x + x2 = 0 + 0.5 1.125x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.125x + x2 = 0.5 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 0.5 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.5 + 0.31640625 Combine like terms: 0.5 + 0.31640625 = 0.81640625 0.31640625 + 1.125x + x2 = 0.81640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.903552018 and -0.903552018.Subproblem 1
x + 0.5625 = 0.903552018 Simplifying x + 0.5625 = 0.903552018 Reorder the terms: 0.5625 + x = 0.903552018 Solving 0.5625 + x = 0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.903552018 + -0.5625 x = 0.903552018 + -0.5625 Combine like terms: 0.903552018 + -0.5625 = 0.341052018 x = 0.341052018 Simplifying x = 0.341052018Subproblem 2
x + 0.5625 = -0.903552018 Simplifying x + 0.5625 = -0.903552018 Reorder the terms: 0.5625 + x = -0.903552018 Solving 0.5625 + x = -0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.903552018 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.903552018 + -0.5625 x = -0.903552018 + -0.5625 Combine like terms: -0.903552018 + -0.5625 = -1.466052018 x = -1.466052018 Simplifying x = -1.466052018Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.341052018, -1.466052018}
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