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Simplifying 3a2 + ab + 5b2 = 0 Reorder the terms: ab + 3a2 + 5b2 = 0 Solving ab + 3a2 + 5b2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333ab + a2 + 1.666666667b2 = 0 Move the constant term to the right: Add '-1.666666667b2' to each side of the equation. 0.3333333333ab + a2 + 1.666666667b2 + -1.666666667b2 = 0 + -1.666666667b2 Combine like terms: 1.666666667b2 + -1.666666667b2 = 0.000000000 0.3333333333ab + a2 + 0.000000000 = 0 + -1.666666667b2 0.3333333333ab + a2 = 0 + -1.666666667b2 Remove the zero: 0.3333333333ab + a2 = -1.666666667b2 The a term is ab. Take half its coefficient (0.5b). Square it (0.25b2) and add it to both sides. Add '0.25b2' to each side of the equation. 0.3333333333ab + a2 + 0.25b2 = -1.666666667b2 + 0.25b2 Combine like terms: -1.666666667b2 + 0.25b2 = -1.416666667b2 0.3333333333ab + a2 + 0.25b2 = -1.416666667b2 Factor a perfect square on the left side: (a + 0.5b)(a + 0.5b) = -1.416666667b2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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