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Simplifying 4x * 4x + 5y * 4x + 4x * 5y + 5y * 5y = 0 Reorder the terms for easier multiplication: 4 * 4x * x + 5y * 4x + 4x * 5y + 5y * 5y = 0 Multiply 4 * 4 16x * x + 5y * 4x + 4x * 5y + 5y * 5y = 0 Multiply x * x 16x2 + 5y * 4x + 4x * 5y + 5y * 5y = 0 Reorder the terms for easier multiplication: 16x2 + 5 * 4y * x + 4x * 5y + 5y * 5y = 0 Multiply 5 * 4 16x2 + 20y * x + 4x * 5y + 5y * 5y = 0 Multiply y * x 16x2 + 20xy + 4x * 5y + 5y * 5y = 0 Reorder the terms for easier multiplication: 16x2 + 20xy + 4 * 5x * y + 5y * 5y = 0 Multiply 4 * 5 16x2 + 20xy + 20x * y + 5y * 5y = 0 Multiply x * y 16x2 + 20xy + 20xy + 5y * 5y = 0 Reorder the terms for easier multiplication: 16x2 + 20xy + 20xy + 5 * 5y * y = 0 Multiply 5 * 5 16x2 + 20xy + 20xy + 25y * y = 0 Multiply y * y 16x2 + 20xy + 20xy + 25y2 = 0 Reorder the terms: 20xy + 20xy + 16x2 + 25y2 = 0 Combine like terms: 20xy + 20xy = 40xy 40xy + 16x2 + 25y2 = 0 Solving 40xy + 16x2 + 25y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + 5y)(4x + 5y) = 0Subproblem 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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