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Simplifying (8x + -3)(x + 2) = 4 Reorder the terms: (-3 + 8x)(x + 2) = 4 Reorder the terms: (-3 + 8x)(2 + x) = 4 Multiply (-3 + 8x) * (2 + x) (-3(2 + x) + 8x * (2 + x)) = 4 ((2 * -3 + x * -3) + 8x * (2 + x)) = 4 ((-6 + -3x) + 8x * (2 + x)) = 4 (-6 + -3x + (2 * 8x + x * 8x)) = 4 (-6 + -3x + (16x + 8x2)) = 4 Combine like terms: -3x + 16x = 13x (-6 + 13x + 8x2) = 4 Solving -6 + 13x + 8x2 = 4 Solving for variable 'x'. Reorder the terms: -6 + -4 + 13x + 8x2 = 4 + -4 Combine like terms: -6 + -4 = -10 -10 + 13x + 8x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -10 + 13x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + 1.625x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.625x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.625x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.625x + x2 = 0 + 1.25 1.625x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.625x + x2 = 1.25 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = 1.25 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = 1.25 + 0.66015625 Combine like terms: 1.25 + 0.66015625 = 1.91015625 0.66015625 + 1.625x + x2 = 1.91015625 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 1.91015625 Calculate the square root of the right side: 1.382084024 Break this problem into two subproblems by setting (x + 0.8125) equal to 1.382084024 and -1.382084024.Subproblem 1
x + 0.8125 = 1.382084024 Simplifying x + 0.8125 = 1.382084024 Reorder the terms: 0.8125 + x = 1.382084024 Solving 0.8125 + x = 1.382084024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 1.382084024 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 1.382084024 + -0.8125 x = 1.382084024 + -0.8125 Combine like terms: 1.382084024 + -0.8125 = 0.569584024 x = 0.569584024 Simplifying x = 0.569584024Subproblem 2
x + 0.8125 = -1.382084024 Simplifying x + 0.8125 = -1.382084024 Reorder the terms: 0.8125 + x = -1.382084024 Solving 0.8125 + x = -1.382084024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -1.382084024 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -1.382084024 + -0.8125 x = -1.382084024 + -0.8125 Combine like terms: -1.382084024 + -0.8125 = -2.194584024 x = -2.194584024 Simplifying x = -2.194584024Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.569584024, -2.194584024}
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