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Simplifying 4s2 + rs + 5r2 = 0 Reorder the terms: rs + 5r2 + 4s2 = 0 Solving rs + 5r2 + 4s2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2rs + r2 + 0.8s2 = 0 Move the constant term to the right: Add '-0.8s2' to each side of the equation. 0.2rs + r2 + 0.8s2 + -0.8s2 = 0 + -0.8s2 Combine like terms: 0.8s2 + -0.8s2 = 0.0 0.2rs + r2 + 0.0 = 0 + -0.8s2 0.2rs + r2 = 0 + -0.8s2 Remove the zero: 0.2rs + r2 = -0.8s2 The r term is rs. Take half its coefficient (0.5s). Square it (0.25s2) and add it to both sides. Add '0.25s2' to each side of the equation. 0.2rs + r2 + 0.25s2 = -0.8s2 + 0.25s2 Combine like terms: -0.8s2 + 0.25s2 = -0.55s2 0.2rs + r2 + 0.25s2 = -0.55s2 Factor a perfect square on the left side: (r + 0.5s)(r + 0.5s) = -0.55s2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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