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Simplifying (5x + y)(5x + y) = 0 Multiply (5x + y) * (5x + y) (5x * (5x + y) + y(5x + y)) = 0 ((5x * 5x + y * 5x) + y(5x + y)) = 0 Reorder the terms: ((5xy + 25x2) + y(5x + y)) = 0 ((5xy + 25x2) + y(5x + y)) = 0 (5xy + 25x2 + (5x * y + y * y)) = 0 (5xy + 25x2 + (5xy + y2)) = 0 Reorder the terms: (5xy + 5xy + 25x2 + y2) = 0 Combine like terms: 5xy + 5xy = 10xy (10xy + 25x2 + y2) = 0 Solving 10xy + 25x2 + y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + y)(5x + y) = 0Subproblem 1
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySubproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySolution
x = {-0.2y, -0.2y}
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