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Simplifying 5m2 + mn + 12n2 = 0 Reorder the terms: mn + 5m2 + 12n2 = 0 Solving mn + 5m2 + 12n2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2mn + m2 + 2.4n2 = 0 Move the constant term to the right: Add '-2.4n2' to each side of the equation. 0.2mn + m2 + 2.4n2 + -2.4n2 = 0 + -2.4n2 Combine like terms: 2.4n2 + -2.4n2 = 0.0 0.2mn + m2 + 0.0 = 0 + -2.4n2 0.2mn + m2 = 0 + -2.4n2 Remove the zero: 0.2mn + m2 = -2.4n2 The m term is mn. Take half its coefficient (0.5n). Square it (0.25n2) and add it to both sides. Add '0.25n2' to each side of the equation. 0.2mn + m2 + 0.25n2 = -2.4n2 + 0.25n2 Combine like terms: -2.4n2 + 0.25n2 = -2.15n2 0.2mn + m2 + 0.25n2 = -2.15n2 Factor a perfect square on the left side: (m + 0.5n)(m + 0.5n) = -2.15n2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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