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Simplifying (x + 3)(x + 4) = 48 Reorder the terms: (3 + x)(x + 4) = 48 Reorder the terms: (3 + x)(4 + x) = 48 Multiply (3 + x) * (4 + x) (3(4 + x) + x(4 + x)) = 48 ((4 * 3 + x * 3) + x(4 + x)) = 48 ((12 + 3x) + x(4 + x)) = 48 (12 + 3x + (4 * x + x * x)) = 48 (12 + 3x + (4x + x2)) = 48 Combine like terms: 3x + 4x = 7x (12 + 7x + x2) = 48 Solving 12 + 7x + x2 = 48 Solving for variable 'x'. Reorder the terms: 12 + -48 + 7x + x2 = 48 + -48 Combine like terms: 12 + -48 = -36 -36 + 7x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -36 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 7x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 7x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 7x + x2 = 0 + 36 7x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 7x + x2 = 36 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 36 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 36 + 12.25 Combine like terms: 36 + 12.25 = 48.25 12.25 + 7x + x2 = 48.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 3.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 3.5 = 6.946221995 Simplifying x + 3.5 = 6.946221995 Reorder the terms: 3.5 + x = 6.946221995 Solving 3.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.946221995 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.946221995 + -3.5 x = 6.946221995 + -3.5 Combine like terms: 6.946221995 + -3.5 = 3.446221995 x = 3.446221995 Simplifying x = 3.446221995Subproblem 2
x + 3.5 = -6.946221995 Simplifying x + 3.5 = -6.946221995 Reorder the terms: 3.5 + x = -6.946221995 Solving 3.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.946221995 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.946221995 + -3.5 x = -6.946221995 + -3.5 Combine like terms: -6.946221995 + -3.5 = -10.446221995 x = -10.446221995 Simplifying x = -10.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.446221995, -10.446221995}
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