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Simplifying a(a + -5) + 3(2a + 7) = 0 Reorder the terms: a(-5 + a) + 3(2a + 7) = 0 (-5 * a + a * a) + 3(2a + 7) = 0 (-5a + a2) + 3(2a + 7) = 0 Reorder the terms: -5a + a2 + 3(7 + 2a) = 0 -5a + a2 + (7 * 3 + 2a * 3) = 0 -5a + a2 + (21 + 6a) = 0 Reorder the terms: 21 + -5a + 6a + a2 = 0 Combine like terms: -5a + 6a = 1a 21 + 1a + a2 = 0 Solving 21 + 1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 1a + -21 + a2 = 0 + -21 Reorder the terms: 21 + -21 + 1a + a2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 1a + a2 = 0 + -21 1a + a2 = 0 + -21 Combine like terms: 0 + -21 = -21 1a + a2 = -21 The a term is 1a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. a + 0.25 + a2 = -21 + 0.25 Reorder the terms: 0.25 + a + a2 = -21 + 0.25 Combine like terms: -21 + 0.25 = -20.75 0.25 + a + a2 = -20.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -20.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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