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Simplifying 2x2 + ax = -4a2 Reorder the terms: ax + 2x2 = -4a2 Solving ax + 2x2 = -4a2 Solving for variable 'a'. Reorder the terms: ax + 4a2 + 2x2 = -4a2 + 4a2 Combine like terms: -4a2 + 4a2 = 0 ax + 4a2 + 2x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25ax + a2 + 0.5x2 = 0 Move the constant term to the right: Add '-0.5x2' to each side of the equation. 0.25ax + a2 + 0.5x2 + -0.5x2 = 0 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 0.25ax + a2 + 0.0 = 0 + -0.5x2 0.25ax + a2 = 0 + -0.5x2 Remove the zero: 0.25ax + a2 = -0.5x2 The a term is ax. Take half its coefficient (0.5x). Square it (0.25x2) and add it to both sides. Add '0.25x2' to each side of the equation. 0.25ax + a2 + 0.25x2 = -0.5x2 + 0.25x2 Combine like terms: -0.5x2 + 0.25x2 = -0.25x2 0.25ax + a2 + 0.25x2 = -0.25x2 Factor a perfect square on the left side: (a + 0.5x)(a + 0.5x) = -0.25x2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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