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Simplifying (x + 9)(x + -5) = x2 + 1 Reorder the terms: (9 + x)(x + -5) = x2 + 1 Reorder the terms: (9 + x)(-5 + x) = x2 + 1 Multiply (9 + x) * (-5 + x) (9(-5 + x) + x(-5 + x)) = x2 + 1 ((-5 * 9 + x * 9) + x(-5 + x)) = x2 + 1 ((-45 + 9x) + x(-5 + x)) = x2 + 1 (-45 + 9x + (-5 * x + x * x)) = x2 + 1 (-45 + 9x + (-5x + x2)) = x2 + 1 Combine like terms: 9x + -5x = 4x (-45 + 4x + x2) = x2 + 1 Reorder the terms: -45 + 4x + x2 = 1 + x2 Add '-1x2' to each side of the equation. -45 + 4x + x2 + -1x2 = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 4x + 0 = 1 + x2 + -1x2 -45 + 4x = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 4x = 1 + 0 -45 + 4x = 1 Solving -45 + 4x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + 4x = 1 + 45 Combine like terms: -45 + 45 = 0 0 + 4x = 1 + 45 4x = 1 + 45 Combine like terms: 1 + 45 = 46 4x = 46 Divide each side by '4'. x = 11.5 Simplifying x = 11.5
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