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Simplifying (x + 4)(x + -1a) = x2 + bx + 8 Reorder the terms: (4 + x)(x + -1a) = x2 + bx + 8 Reorder the terms: (4 + x)(-1a + x) = x2 + bx + 8 Multiply (4 + x) * (-1a + x) (4(-1a + x) + x(-1a + x)) = x2 + bx + 8 ((-1a * 4 + x * 4) + x(-1a + x)) = x2 + bx + 8 ((-4a + 4x) + x(-1a + x)) = x2 + bx + 8 (-4a + 4x + (-1a * x + x * x)) = x2 + bx + 8 (-4a + 4x + (-1ax + x2)) = x2 + bx + 8 Reorder the terms: (-4a + -1ax + 4x + x2) = x2 + bx + 8 (-4a + -1ax + 4x + x2) = x2 + bx + 8 Reorder the terms: -4a + -1ax + 4x + x2 = 8 + bx + x2 Add '-1x2' to each side of the equation. -4a + -1ax + 4x + x2 + -1x2 = 8 + bx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4a + -1ax + 4x + 0 = 8 + bx + x2 + -1x2 -4a + -1ax + 4x = 8 + bx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4a + -1ax + 4x = 8 + bx + 0 -4a + -1ax + 4x = 8 + bx Solving -4a + -1ax + 4x = 8 + bx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4x' to each side of the equation. -4a + -1ax + 4x + -4x = 8 + bx + -4x Combine like terms: 4x + -4x = 0 -4a + -1ax + 0 = 8 + bx + -4x -4a + -1ax = 8 + bx + -4x Reorder the terms: -8 + -4a + -1ax + -1bx + 4x = 8 + bx + -4x + -8 + -1bx + 4x Reorder the terms: -8 + -4a + -1ax + -1bx + 4x = 8 + -8 + bx + -1bx + -4x + 4x Combine like terms: 8 + -8 = 0 -8 + -4a + -1ax + -1bx + 4x = 0 + bx + -1bx + -4x + 4x -8 + -4a + -1ax + -1bx + 4x = bx + -1bx + -4x + 4x Combine like terms: bx + -1bx = 0 -8 + -4a + -1ax + -1bx + 4x = 0 + -4x + 4x -8 + -4a + -1ax + -1bx + 4x = -4x + 4x Combine like terms: -4x + 4x = 0 -8 + -4a + -1ax + -1bx + 4x = 0 The solution to this equation could not be determined.
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