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Simplifying (5x + 4y)(5x + 4y) = 0 Multiply (5x + 4y) * (5x + 4y) (5x * (5x + 4y) + 4y * (5x + 4y)) = 0 ((5x * 5x + 4y * 5x) + 4y * (5x + 4y)) = 0 Reorder the terms: ((20xy + 25x2) + 4y * (5x + 4y)) = 0 ((20xy + 25x2) + 4y * (5x + 4y)) = 0 (20xy + 25x2 + (5x * 4y + 4y * 4y)) = 0 (20xy + 25x2 + (20xy + 16y2)) = 0 Reorder the terms: (20xy + 20xy + 25x2 + 16y2) = 0 Combine like terms: 20xy + 20xy = 40xy (40xy + 25x2 + 16y2) = 0 Solving 40xy + 25x2 + 16y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + 4y)(5x + 4y) = 0Subproblem 1
Set the factor '(5x + 4y)' equal to zero and attempt to solve: Simplifying 5x + 4y = 0 Solving 5x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 5x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 5x + 0 = 0 + -4y 5x = 0 + -4y Remove the zero: 5x = -4y Divide each side by '5'. x = -0.8y Simplifying x = -0.8ySubproblem 2
Set the factor '(5x + 4y)' equal to zero and attempt to solve: Simplifying 5x + 4y = 0 Solving 5x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 5x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 5x + 0 = 0 + -4y 5x = 0 + -4y Remove the zero: 5x = -4y Divide each side by '5'. x = -0.8y Simplifying x = -0.8ySolution
x = {-0.8y, -0.8y}
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