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Simplifying 0 = 16x2 + 40xy + 25y2 Reorder the terms: 0 = 40xy + 16x2 + 25y2 Solving 0 = 40xy + 16x2 + 25y2 Solving for variable 'x'. Remove the zero: -40xy + -16x2 + -25y2 = 40xy + 16x2 + 25y2 + -40xy + -16x2 + -25y2 Reorder the terms: -40xy + -16x2 + -25y2 = 40xy + -40xy + 16x2 + -16x2 + 25y2 + -25y2 Combine like terms: 40xy + -40xy = 0 -40xy + -16x2 + -25y2 = 0 + 16x2 + -16x2 + 25y2 + -25y2 -40xy + -16x2 + -25y2 = 16x2 + -16x2 + 25y2 + -25y2 Combine like terms: 16x2 + -16x2 = 0 -40xy + -16x2 + -25y2 = 0 + 25y2 + -25y2 -40xy + -16x2 + -25y2 = 25y2 + -25y2 Combine like terms: 25y2 + -25y2 = 0 -40xy + -16x2 + -25y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40xy + 16x2 + 25y2) = 0 Factor a trinomial. -1((4x + 5y)(4x + 5y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4x + 5y)' equal to zero and attempt to solve: Simplifying 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySubproblem 2
Set the factor '(4x + 5y)' equal to zero and attempt to solve: Simplifying 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySolution
x = {-1.25y, -1.25y}
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