Question

10xy +0.25x^2+100y^2
=
(_+_)^2

Answer 1

(.5x+10y)²
or else (1/2x+10y)²

Answer 2

Simplifying (5x + 10y)(5x + -10y) = 0 Multiply (5x + 10y) * (5x + -10y) (5x * (5x + -10y) + 10y * (5x + -10y)) = 0 ((5x * 5x + -10y * 5x) + 10y * (5x + -10y)) = 0 Reorder the terms: ((-50xy + 25x2) + 10y * (5x + -10y)) = 0 ((-50xy + 25x2) + 10y * (5x + -10y)) = 0 (-50xy + 25x2 + (5x * 10y + -10y * 10y)) = 0 (-50xy + 25x2 + (50xy + -100y2)) = 0 Reorder the terms: (-50xy + 50xy + 25x2 + -100y2) = 0 Combine like terms: -50xy + 50xy = 0 (0 + 25x2 + -100y2) = 0 (25x2 + -100y2) = 0 Solving 25x2 + -100y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100y2' to each side of the equation. 25x2 + -100y2 + 100y2 = 0 + 100y2 Combine like terms: -100y2 + 100y2 = 0 25x2 + 0 = 0 + 100y2 25x2 = 0 + 100y2 Remove the zero: 25x2 = 100y2 Divide each side by '25'. x2 = 4y2 Simplifying x2 = 4y2 Take the square root of each side: x = {-2y, 2y}