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Simplifying (a + 5)(a + 7) = -20 Reorder the terms: (5 + a)(a + 7) = -20 Reorder the terms: (5 + a)(7 + a) = -20 Multiply (5 + a) * (7 + a) (5(7 + a) + a(7 + a)) = -20 ((7 * 5 + a * 5) + a(7 + a)) = -20 ((35 + 5a) + a(7 + a)) = -20 (35 + 5a + (7 * a + a * a)) = -20 (35 + 5a + (7a + a2)) = -20 Combine like terms: 5a + 7a = 12a (35 + 12a + a2) = -20 Solving 35 + 12a + a2 = -20 Solving for variable 'a'. Reorder the terms: 35 + 20 + 12a + a2 = -20 + 20 Combine like terms: 35 + 20 = 55 55 + 12a + a2 = -20 + 20 Combine like terms: -20 + 20 = 0 55 + 12a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + 12a + -55 + a2 = 0 + -55 Reorder the terms: 55 + -55 + 12a + a2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 12a + a2 = 0 + -55 12a + a2 = 0 + -55 Combine like terms: 0 + -55 = -55 12a + a2 = -55 The a term is 12a. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12a + 36 + a2 = -55 + 36 Reorder the terms: 36 + 12a + a2 = -55 + 36 Combine like terms: -55 + 36 = -19 36 + 12a + a2 = -19 Factor a perfect square on the left side: (a + 6)(a + 6) = -19 Can't calculate square root of the right side. The solution to this equation could not be determined.
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