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Simplifying (x + 12)(x + -5) = x2 + 31 Reorder the terms: (12 + x)(x + -5) = x2 + 31 Reorder the terms: (12 + x)(-5 + x) = x2 + 31 Multiply (12 + x) * (-5 + x) (12(-5 + x) + x(-5 + x)) = x2 + 31 ((-5 * 12 + x * 12) + x(-5 + x)) = x2 + 31 ((-60 + 12x) + x(-5 + x)) = x2 + 31 (-60 + 12x + (-5 * x + x * x)) = x2 + 31 (-60 + 12x + (-5x + x2)) = x2 + 31 Combine like terms: 12x + -5x = 7x (-60 + 7x + x2) = x2 + 31 Reorder the terms: -60 + 7x + x2 = 31 + x2 Add '-1x2' to each side of the equation. -60 + 7x + x2 + -1x2 = 31 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + 7x + 0 = 31 + x2 + -1x2 -60 + 7x = 31 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + 7x = 31 + 0 -60 + 7x = 31 Solving -60 + 7x = 31 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + 7x = 31 + 60 Combine like terms: -60 + 60 = 0 0 + 7x = 31 + 60 7x = 31 + 60 Combine like terms: 31 + 60 = 91 7x = 91 Divide each side by '7'. x = 13 Simplifying x = 13
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