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Simplifying a2 + a + -3 + -3a2 + -5 = 0 Reorder the terms: -3 + -5 + a + a2 + -3a2 = 0 Combine like terms: -3 + -5 = -8 -8 + a + a2 + -3a2 = 0 Combine like terms: a2 + -3a2 = -2a2 -8 + a + -2a2 = 0 Solving -8 + a + -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'. 4 + -0.5a + a2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -0.5a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + -0.5a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -0.5a + a2 = 0 + -4 -0.5a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 -0.5a + a2 = -4 The a term is a. 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. -0.5a + 0.25 + a2 = -4 + 0.25 Reorder the terms: 0.25 + -0.5a + a2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -0.5a + a2 = -3.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -3.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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