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Simplifying 2x2 + 2xy + 18y2 = 0 Reorder the terms: 2xy + 2x2 + 18y2 = 0 Solving 2xy + 2x2 + 18y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(xy + x2 + 9y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(xy + x2 + 9y2)' equal to zero and attempt to solve: Simplifying xy + x2 + 9y2 = 0 Solving xy + x2 + 9y2 = 0 Begin completing the square. Move the constant term to the right: Add '-9y2' to each side of the equation. xy + x2 + 9y2 + -9y2 = 0 + -9y2 Combine like terms: 9y2 + -9y2 = 0 xy + x2 + 0 = 0 + -9y2 xy + x2 = 0 + -9y2 Remove the zero: xy + x2 = -9y2 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. xy + x2 + 0.25y2 = -9y2 + 0.25y2 Combine like terms: -9y2 + 0.25y2 = -8.75y2 xy + x2 + 0.25y2 = -8.75y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -8.75y2 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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