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Simplifying a + -4a2 = 3 Solving a + -4a2 = 3 Solving for variable 'a'. Reorder the terms: -3 + a + -4a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -0.25a + a2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.25a + -0.75 + a2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.25a + a2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.25a + a2 = 0 + -0.75 -0.25a + a2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.25a + a2 = -0.75 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. -0.25a + 0.25 + a2 = -0.75 + 0.25 Reorder the terms: 0.25 + -0.25a + a2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + -0.25a + a2 = -0.5 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -0.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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