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Simplifying 2a(2a + -5) + 18 = a(7 + -1a) + -12 Reorder the terms: 2a(-5 + 2a) + 18 = a(7 + -1a) + -12 (-5 * 2a + 2a * 2a) + 18 = a(7 + -1a) + -12 (-10a + 4a2) + 18 = a(7 + -1a) + -12 Reorder the terms: 18 + -10a + 4a2 = a(7 + -1a) + -12 18 + -10a + 4a2 = (7 * a + -1a * a) + -12 18 + -10a + 4a2 = (7a + -1a2) + -12 Reorder the terms: 18 + -10a + 4a2 = -12 + 7a + -1a2 Solving 18 + -10a + 4a2 = -12 + 7a + -1a2 Solving for variable 'a'. Reorder the terms: 18 + 12 + -10a + -7a + 4a2 + a2 = -12 + 7a + -1a2 + 12 + -7a + a2 Combine like terms: 18 + 12 = 30 30 + -10a + -7a + 4a2 + a2 = -12 + 7a + -1a2 + 12 + -7a + a2 Combine like terms: -10a + -7a = -17a 30 + -17a + 4a2 + a2 = -12 + 7a + -1a2 + 12 + -7a + a2 Combine like terms: 4a2 + a2 = 5a2 30 + -17a + 5a2 = -12 + 7a + -1a2 + 12 + -7a + a2 Reorder the terms: 30 + -17a + 5a2 = -12 + 12 + 7a + -7a + -1a2 + a2 Combine like terms: -12 + 12 = 0 30 + -17a + 5a2 = 0 + 7a + -7a + -1a2 + a2 30 + -17a + 5a2 = 7a + -7a + -1a2 + a2 Combine like terms: 7a + -7a = 0 30 + -17a + 5a2 = 0 + -1a2 + a2 30 + -17a + 5a2 = -1a2 + a2 Combine like terms: -1a2 + a2 = 0 30 + -17a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + -3.4a + a2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -3.4a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -3.4a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -3.4a + a2 = 0 + -6 -3.4a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -3.4a + a2 = -6 The a term is -3.4a. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4a + 2.89 + a2 = -6 + 2.89 Reorder the terms: 2.89 + -3.4a + a2 = -6 + 2.89 Combine like terms: -6 + 2.89 = -3.11 2.89 + -3.4a + a2 = -3.11 Factor a perfect square on the left side: (a + -1.7)(a + -1.7) = -3.11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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