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Simplifying (8a2 + 2a + -3) + (-5a2 + 4a + 7) = 0 Reorder the terms: (-3 + 2a + 8a2) + (-5a2 + 4a + 7) = 0 Remove parenthesis around (-3 + 2a + 8a2) -3 + 2a + 8a2 + (-5a2 + 4a + 7) = 0 Reorder the terms: -3 + 2a + 8a2 + (7 + 4a + -5a2) = 0 Remove parenthesis around (7 + 4a + -5a2) -3 + 2a + 8a2 + 7 + 4a + -5a2 = 0 Reorder the terms: -3 + 7 + 2a + 4a + 8a2 + -5a2 = 0 Combine like terms: -3 + 7 = 4 4 + 2a + 4a + 8a2 + -5a2 = 0 Combine like terms: 2a + 4a = 6a 4 + 6a + 8a2 + -5a2 = 0 Combine like terms: 8a2 + -5a2 = 3a2 4 + 6a + 3a2 = 0 Solving 4 + 6a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 2a + a2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2a + -1.333333333 + a2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2a + a2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2a + a2 = 0 + -1.333333333 2a + a2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2a + a2 = -1.333333333 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 = -1.333333333 + 1 Reorder the terms: 1 + 2a + a2 = -1.333333333 + 1 Combine like terms: -1.333333333 + 1 = -0.333333333 1 + 2a + a2 = -0.333333333 Factor a perfect square on the left side: (a + 1)(a + 1) = -0.333333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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