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Simplifying (x + 1)(x + 5) + 8 = 0 Reorder the terms: (1 + x)(x + 5) + 8 = 0 Reorder the terms: (1 + x)(5 + x) + 8 = 0 Multiply (1 + x) * (5 + x) (1(5 + x) + x(5 + x)) + 8 = 0 ((5 * 1 + x * 1) + x(5 + x)) + 8 = 0 ((5 + 1x) + x(5 + x)) + 8 = 0 (5 + 1x + (5 * x + x * x)) + 8 = 0 (5 + 1x + (5x + x2)) + 8 = 0 Combine like terms: 1x + 5x = 6x (5 + 6x + x2) + 8 = 0 Reorder the terms: 5 + 8 + 6x + x2 = 0 Combine like terms: 5 + 8 = 13 13 + 6x + x2 = 0 Solving 13 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 6x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 6x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6x + x2 = 0 + -13 6x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 6x + x2 = -13 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -13 + 9 Reorder the terms: 9 + 6x + x2 = -13 + 9 Combine like terms: -13 + 9 = -4 9 + 6x + x2 = -4 Factor a perfect square on the left side: (x + 3)(x + 3) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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