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Simplifying (4x + -1)(2x + 3) = 18 + -4 Reorder the terms: (-1 + 4x)(2x + 3) = 18 + -4 Reorder the terms: (-1 + 4x)(3 + 2x) = 18 + -4 Multiply (-1 + 4x) * (3 + 2x) (-1(3 + 2x) + 4x * (3 + 2x)) = 18 + -4 ((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = 18 + -4 ((-3 + -2x) + 4x * (3 + 2x)) = 18 + -4 (-3 + -2x + (3 * 4x + 2x * 4x)) = 18 + -4 (-3 + -2x + (12x + 8x2)) = 18 + -4 Combine like terms: -2x + 12x = 10x (-3 + 10x + 8x2) = 18 + -4 Combine like terms: 18 + -4 = 14 -3 + 10x + 8x2 = 14 Solving -3 + 10x + 8x2 = 14 Solving for variable 'x'. Reorder the terms: -3 + -14 + 10x + 8x2 = 14 + -14 Combine like terms: -3 + -14 = -17 -17 + 10x + 8x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -17 + 10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + 1.25x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 1.25x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 1.25x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 1.25x + x2 = 0 + 2.125 1.25x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 1.25x + x2 = 2.125 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2.125 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2.125 + 0.390625 Combine like terms: 2.125 + 0.390625 = 2.515625 0.390625 + 1.25x + x2 = 2.515625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + 0.625) equal to 1.586072193 and -1.586072193.Subproblem 1
x + 0.625 = 1.586072193 Simplifying x + 0.625 = 1.586072193 Reorder the terms: 0.625 + x = 1.586072193 Solving 0.625 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.586072193 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.586072193 + -0.625 x = 1.586072193 + -0.625 Combine like terms: 1.586072193 + -0.625 = 0.961072193 x = 0.961072193 Simplifying x = 0.961072193Subproblem 2
x + 0.625 = -1.586072193 Simplifying x + 0.625 = -1.586072193 Reorder the terms: 0.625 + x = -1.586072193 Solving 0.625 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.586072193 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.586072193 + -0.625 x = -1.586072193 + -0.625 Combine like terms: -1.586072193 + -0.625 = -2.211072193 x = -2.211072193 Simplifying x = -2.211072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.961072193, -2.211072193}
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