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Simplifying (12 + x)(4 + x) = 56 Multiply (12 + x) * (4 + x) (12(4 + x) + x(4 + x)) = 56 ((4 * 12 + x * 12) + x(4 + x)) = 56 ((48 + 12x) + x(4 + x)) = 56 (48 + 12x + (4 * x + x * x)) = 56 (48 + 12x + (4x + x2)) = 56 Combine like terms: 12x + 4x = 16x (48 + 16x + x2) = 56 Solving 48 + 16x + x2 = 56 Solving for variable 'x'. Reorder the terms: 48 + -56 + 16x + x2 = 56 + -56 Combine like terms: 48 + -56 = -8 -8 + 16x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -8 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 16x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 16x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 16x + x2 = 0 + 8 16x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 16x + x2 = 8 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 8 + 64 Reorder the terms: 64 + 16x + x2 = 8 + 64 Combine like terms: 8 + 64 = 72 64 + 16x + x2 = 72 Factor a perfect square on the left side: (x + 8)(x + 8) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 8) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 8 = 8.485281374 Simplifying x + 8 = 8.485281374 Reorder the terms: 8 + x = 8.485281374 Solving 8 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.485281374 + -8 x = 8.485281374 + -8 Combine like terms: 8.485281374 + -8 = 0.485281374 x = 0.485281374 Simplifying x = 0.485281374Subproblem 2
x + 8 = -8.485281374 Simplifying x + 8 = -8.485281374 Reorder the terms: 8 + x = -8.485281374 Solving 8 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.485281374 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.485281374 + -8 x = -8.485281374 + -8 Combine like terms: -8.485281374 + -8 = -16.485281374 x = -16.485281374 Simplifying x = -16.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.485281374, -16.485281374}
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