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Simplifying 48x2 + 6xy + 60y2 = 0 Reorder the terms: 6xy + 48x2 + 60y2 = 0 Solving 6xy + 48x2 + 60y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(xy + 8x2 + 10y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(xy + 8x2 + 10y2)' equal to zero and attempt to solve: Simplifying xy + 8x2 + 10y2 = 0 Solving xy + 8x2 + 10y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125xy + x2 + 1.25y2 = 0 Move the constant term to the right: Add '-1.25y2' to each side of the equation. 0.125xy + x2 + 1.25y2 + -1.25y2 = 0 + -1.25y2 Combine like terms: 1.25y2 + -1.25y2 = 0.00 0.125xy + x2 + 0.00 = 0 + -1.25y2 0.125xy + x2 = 0 + -1.25y2 Remove the zero: 0.125xy + x2 = -1.25y2 The x term is xy. Take half its coefficient (0.5y). Square it (0.25y2) and add it to both sides. Add '0.25y2' to each side of the equation. 0.125xy + x2 + 0.25y2 = -1.25y2 + 0.25y2 Combine like terms: -1.25y2 + 0.25y2 = -1y2 0.125xy + x2 + 0.25y2 = -1y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -1y2 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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