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Simplifying (x + 4)(x + 8) = 28 Reorder the terms: (4 + x)(x + 8) = 28 Reorder the terms: (4 + x)(8 + x) = 28 Multiply (4 + x) * (8 + x) (4(8 + x) + x(8 + x)) = 28 ((8 * 4 + x * 4) + x(8 + x)) = 28 ((32 + 4x) + x(8 + x)) = 28 (32 + 4x + (8 * x + x * x)) = 28 (32 + 4x + (8x + x2)) = 28 Combine like terms: 4x + 8x = 12x (32 + 12x + x2) = 28 Solving 32 + 12x + x2 = 28 Solving for variable 'x'. Reorder the terms: 32 + -28 + 12x + x2 = 28 + -28 Combine like terms: 32 + -28 = 4 4 + 12x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 4 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 12x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 12x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 12x + x2 = 0 + -4 12x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 12x + x2 = -4 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -4 + 36 Reorder the terms: 36 + 12x + x2 = -4 + 36 Combine like terms: -4 + 36 = 32 36 + 12x + x2 = 32 Factor a perfect square on the left side: (x + 6)(x + 6) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 6) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 6 = 5.656854249 Simplifying x + 6 = 5.656854249 Reorder the terms: 6 + x = 5.656854249 Solving 6 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.656854249 + -6 x = 5.656854249 + -6 Combine like terms: 5.656854249 + -6 = -0.343145751 x = -0.343145751 Simplifying x = -0.343145751Subproblem 2
x + 6 = -5.656854249 Simplifying x + 6 = -5.656854249 Reorder the terms: 6 + x = -5.656854249 Solving 6 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.656854249 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.656854249 + -6 x = -5.656854249 + -6 Combine like terms: -5.656854249 + -6 = -11.656854249 x = -11.656854249 Simplifying x = -11.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.343145751, -11.656854249}
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