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Simplifying
(5x + -7y)(5x + 7y) = 0
Multiply (5x + -7y) * (5x + 7y)
(5x * (5x + 7y) + -7y * (5x + 7y)) = 0
((5x * 5x + 7y * 5x) + -7y * (5x + 7y)) = 0
Reorder the terms:
((35xy + 25x2) + -7y * (5x + 7y)) = 0
((35xy + 25x2) + -7y * (5x + 7y)) = 0
(35xy + 25x2 + (5x * -7y + 7y * -7y)) = 0
(35xy + 25x2 + (-35xy + -49y2)) = 0
Reorder the terms:
(35xy + -35xy + 25x2 + -49y2) = 0
Combine like terms: 35xy + -35xy = 0
(0 + 25x2 + -49y2) = 0
(25x2 + -49y2) = 0
Solving
25x2 + -49y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '49y2' to each side of the equation.
25x2 + -49y2 + 49y2 = 0 + 49y2
Combine like terms: -49y2 + 49y2 = 0
25x2 + 0 = 0 + 49y2
25x2 = 0 + 49y2
Remove the zero:
25x2 = 49y2
Divide each side by '25'.
x2 = 1.96y2
Simplifying
x2 = 1.96y2
Take the square root of each side:
x = {-1.4y, 1.4y}
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