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Simplifying (x + 5)(x + 3) + -1x = x2 + 1 Reorder the terms: (5 + x)(x + 3) + -1x = x2 + 1 Reorder the terms: (5 + x)(3 + x) + -1x = x2 + 1 Multiply (5 + x) * (3 + x) (5(3 + x) + x(3 + x)) + -1x = x2 + 1 ((3 * 5 + x * 5) + x(3 + x)) + -1x = x2 + 1 ((15 + 5x) + x(3 + x)) + -1x = x2 + 1 (15 + 5x + (3 * x + x * x)) + -1x = x2 + 1 (15 + 5x + (3x + x2)) + -1x = x2 + 1 Combine like terms: 5x + 3x = 8x (15 + 8x + x2) + -1x = x2 + 1 Reorder the terms: 15 + 8x + -1x + x2 = x2 + 1 Combine like terms: 8x + -1x = 7x 15 + 7x + x2 = x2 + 1 Reorder the terms: 15 + 7x + x2 = 1 + x2 Add '-1x2' to each side of the equation. 15 + 7x + x2 + -1x2 = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + 7x + 0 = 1 + x2 + -1x2 15 + 7x = 1 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + 7x = 1 + 0 15 + 7x = 1 Solving 15 + 7x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 7x = 1 + -15 Combine like terms: 15 + -15 = 0 0 + 7x = 1 + -15 7x = 1 + -15 Combine like terms: 1 + -15 = -14 7x = -14 Divide each side by '7'. x = -2 Simplifying x = -2
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