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Simplifying x2 + 8a * x + 8a2 = 0 Multiply a * x x2 + 8ax + 8a2 = 0 Reorder the terms: 8ax + 8a2 + x2 = 0 Solving 8ax + 8a2 + x2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. ax + a2 + 0.125x2 = 0 Move the constant term to the right: Add '-1x2' to each side of the equation. ax + a2 + 0.125x2 + -1x2 = 0 + -1x2 Combine like terms: 0.125x2 + -1x2 = -0.875x2 ax + a2 + -0.875x2 = 0 + -1x2 Remove the zero: ax + a2 + -0.875x2 = -1x2 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. x2 + a2 + -0.875x2 + 0.25x2 = -1x2 + 0.25x2 Reorder the terms: a2 + x2 + -0.875x2 + 0.25x2 = -1x2 + 0.25x2 Combine like terms: x2 + -0.875x2 = 0.125x2 a2 + 0.125x2 + 0.25x2 = -1x2 + 0.25x2 Combine like terms: 0.125x2 + 0.25x2 = 0.375x2 a2 + 0.375x2 = -1x2 + 0.25x2 Combine like terms: -1x2 + 0.25x2 = -0.75x2 a2 + 0.375x2 = -0.75x2 Factor a perfect square on the left side: (a + 0.5x)(a + 0.5x) = -0.75x2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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