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Simplifying (x + -4)(x + 8) = 39 Reorder the terms: (-4 + x)(x + 8) = 39 Reorder the terms: (-4 + x)(8 + x) = 39 Multiply (-4 + x) * (8 + x) (-4(8 + x) + x(8 + x)) = 39 ((8 * -4 + x * -4) + x(8 + x)) = 39 ((-32 + -4x) + x(8 + x)) = 39 (-32 + -4x + (8 * x + x * x)) = 39 (-32 + -4x + (8x + x2)) = 39 Combine like terms: -4x + 8x = 4x (-32 + 4x + x2) = 39 Solving -32 + 4x + x2 = 39 Solving for variable 'x'. Reorder the terms: -32 + -39 + 4x + x2 = 39 + -39 Combine like terms: -32 + -39 = -71 -71 + 4x + x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -71 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 4x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 4x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 4x + x2 = 0 + 71 4x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 4x + x2 = 71 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 71 + 4 Reorder the terms: 4 + 4x + x2 = 71 + 4 Combine like terms: 71 + 4 = 75 4 + 4x + x2 = 75 Factor a perfect square on the left side: (x + 2)(x + 2) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 2) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 2 = 8.660254038 Simplifying x + 2 = 8.660254038 Reorder the terms: 2 + x = 8.660254038 Solving 2 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.660254038 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.660254038 + -2 x = 8.660254038 + -2 Combine like terms: 8.660254038 + -2 = 6.660254038 x = 6.660254038 Simplifying x = 6.660254038Subproblem 2
x + 2 = -8.660254038 Simplifying x + 2 = -8.660254038 Reorder the terms: 2 + x = -8.660254038 Solving 2 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.660254038 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.660254038 + -2 x = -8.660254038 + -2 Combine like terms: -8.660254038 + -2 = -10.660254038 x = -10.660254038 Simplifying x = -10.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.660254038, -10.660254038}
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