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Simplifying (x + 4)(2x + -1) = 24 Reorder the terms: (4 + x)(2x + -1) = 24 Reorder the terms: (4 + x)(-1 + 2x) = 24 Multiply (4 + x) * (-1 + 2x) (4(-1 + 2x) + x(-1 + 2x)) = 24 ((-1 * 4 + 2x * 4) + x(-1 + 2x)) = 24 ((-4 + 8x) + x(-1 + 2x)) = 24 (-4 + 8x + (-1 * x + 2x * x)) = 24 (-4 + 8x + (-1x + 2x2)) = 24 Combine like terms: 8x + -1x = 7x (-4 + 7x + 2x2) = 24 Solving -4 + 7x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: -4 + -24 + 7x + 2x2 = 24 + -24 Combine like terms: -4 + -24 = -28 -28 + 7x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -28 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + 3.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 3.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 3.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3.5x + x2 = 0 + 14 3.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 3.5x + x2 = 14 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 14 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 14 + 3.0625 Combine like terms: 14 + 3.0625 = 17.0625 3.0625 + 3.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + 1.75) equal to 4.13067791 and -4.13067791.Subproblem 1
x + 1.75 = 4.13067791 Simplifying x + 1.75 = 4.13067791 Reorder the terms: 1.75 + x = 4.13067791 Solving 1.75 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.13067791 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.13067791 + -1.75 x = 4.13067791 + -1.75 Combine like terms: 4.13067791 + -1.75 = 2.38067791 x = 2.38067791 Simplifying x = 2.38067791Subproblem 2
x + 1.75 = -4.13067791 Simplifying x + 1.75 = -4.13067791 Reorder the terms: 1.75 + x = -4.13067791 Solving 1.75 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.13067791 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.13067791 + -1.75 x = -4.13067791 + -1.75 Combine like terms: -4.13067791 + -1.75 = -5.88067791 x = -5.88067791 Simplifying x = -5.88067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.38067791, -5.88067791}
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