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Simplifying (4a2 + -5a) + (-2a2 + 9a + 7) = 0 Reorder the terms: (-5a + 4a2) + (-2a2 + 9a + 7) = 0 Remove parenthesis around (-5a + 4a2) -5a + 4a2 + (-2a2 + 9a + 7) = 0 Reorder the terms: -5a + 4a2 + (7 + 9a + -2a2) = 0 Remove parenthesis around (7 + 9a + -2a2) -5a + 4a2 + 7 + 9a + -2a2 = 0 Reorder the terms: 7 + -5a + 9a + 4a2 + -2a2 = 0 Combine like terms: -5a + 9a = 4a 7 + 4a + 4a2 + -2a2 = 0 Combine like terms: 4a2 + -2a2 = 2a2 7 + 4a + 2a2 = 0 Solving 7 + 4a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 2a + a2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 2a + -3.5 + a2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 2a + a2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 2a + a2 = 0 + -3.5 2a + a2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 2a + a2 = -3.5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -3.5 + 1 Reorder the terms: 1 + 2a + a2 = -3.5 + 1 Combine like terms: -3.5 + 1 = -2.5 1 + 2a + a2 = -2.5 Factor a perfect square on the left side: (a + 1)(a + 1) = -2.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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