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Simplifying (x + -9)(x + 7) = (x + 4) * 2 Reorder the terms: (-9 + x)(x + 7) = (x + 4) * 2 Reorder the terms: (-9 + x)(7 + x) = (x + 4) * 2 Multiply (-9 + x) * (7 + x) (-9(7 + x) + x(7 + x)) = (x + 4) * 2 ((7 * -9 + x * -9) + x(7 + x)) = (x + 4) * 2 ((-63 + -9x) + x(7 + x)) = (x + 4) * 2 (-63 + -9x + (7 * x + x * x)) = (x + 4) * 2 (-63 + -9x + (7x + x2)) = (x + 4) * 2 Combine like terms: -9x + 7x = -2x (-63 + -2x + x2) = (x + 4) * 2 Reorder the terms: -63 + -2x + x2 = (4 + x) * 2 Reorder the terms for easier multiplication: -63 + -2x + x2 = 2(4 + x) -63 + -2x + x2 = (4 * 2 + x * 2) -63 + -2x + x2 = (8 + 2x) Solving -63 + -2x + x2 = 8 + 2x Solving for variable 'x'. Reorder the terms: -63 + -8 + -2x + -2x + x2 = 8 + 2x + -8 + -2x Combine like terms: -63 + -8 = -71 -71 + -2x + -2x + x2 = 8 + 2x + -8 + -2x Combine like terms: -2x + -2x = -4x -71 + -4x + x2 = 8 + 2x + -8 + -2x Reorder the terms: -71 + -4x + x2 = 8 + -8 + 2x + -2x Combine like terms: 8 + -8 = 0 -71 + -4x + x2 = 0 + 2x + -2x -71 + -4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 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 = 10.660254038 x = 10.660254038 Simplifying x = 10.660254038Subproblem 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 = -6.660254038 x = -6.660254038 Simplifying x = -6.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.660254038, -6.660254038}
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