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Simplifying (4x + 2)(x + 4) = 9 Reorder the terms: (2 + 4x)(x + 4) = 9 Reorder the terms: (2 + 4x)(4 + x) = 9 Multiply (2 + 4x) * (4 + x) (2(4 + x) + 4x * (4 + x)) = 9 ((4 * 2 + x * 2) + 4x * (4 + x)) = 9 ((8 + 2x) + 4x * (4 + x)) = 9 (8 + 2x + (4 * 4x + x * 4x)) = 9 (8 + 2x + (16x + 4x2)) = 9 Combine like terms: 2x + 16x = 18x (8 + 18x + 4x2) = 9 Solving 8 + 18x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: 8 + -9 + 18x + 4x2 = 9 + -9 Combine like terms: 8 + -9 = -1 -1 + 18x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -1 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 4.5x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 4.5x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 4.5x + x2 = 0 + 0.25 4.5x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 4.5x + x2 = 0.25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 0.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 0.25 + 5.0625 Combine like terms: 0.25 + 5.0625 = 5.3125 5.0625 + 4.5x + x2 = 5.3125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (x + 2.25) equal to 2.304886114 and -2.304886114.Subproblem 1
x + 2.25 = 2.304886114 Simplifying x + 2.25 = 2.304886114 Reorder the terms: 2.25 + x = 2.304886114 Solving 2.25 + x = 2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.304886114 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.304886114 + -2.25 x = 2.304886114 + -2.25 Combine like terms: 2.304886114 + -2.25 = 0.054886114 x = 0.054886114 Simplifying x = 0.054886114Subproblem 2
x + 2.25 = -2.304886114 Simplifying x + 2.25 = -2.304886114 Reorder the terms: 2.25 + x = -2.304886114 Solving 2.25 + x = -2.304886114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.304886114 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.304886114 + -2.25 x = -2.304886114 + -2.25 Combine like terms: -2.304886114 + -2.25 = -4.554886114 x = -4.554886114 Simplifying x = -4.554886114Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.054886114, -4.554886114}
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