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Simplifying 10x2 + 10xy + 16y2 = 0 Reorder the terms: 10xy + 10x2 + 16y2 = 0 Solving 10xy + 10x2 + 16y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5xy + 5x2 + 8y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5xy + 5x2 + 8y2)' equal to zero and attempt to solve: Simplifying 5xy + 5x2 + 8y2 = 0 Solving 5xy + 5x2 + 8y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. xy + x2 + 1.6y2 = 0 Move the constant term to the right: Add '-1.6y2' to each side of the equation. xy + x2 + 1.6y2 + -1.6y2 = 0 + -1.6y2 Combine like terms: 1.6y2 + -1.6y2 = 0.0 xy + x2 + 0.0 = 0 + -1.6y2 xy + x2 = 0 + -1.6y2 Remove the zero: xy + x2 = -1.6y2 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. y2 + x2 + 0.25y2 = -1.6y2 + 0.25y2 Reorder the terms: x2 + y2 + 0.25y2 = -1.6y2 + 0.25y2 Combine like terms: y2 + 0.25y2 = 1.25y2 x2 + 1.25y2 = -1.6y2 + 0.25y2 Combine like terms: -1.6y2 + 0.25y2 = -1.35y2 x2 + 1.25y2 = -1.35y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -1.35y2 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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