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Simplifying
(5q + -8r)(5q + 8r) = 0
Multiply (5q + -8r) * (5q + 8r)
(5q * (5q + 8r) + -8r * (5q + 8r)) = 0
((5q * 5q + 8r * 5q) + -8r * (5q + 8r)) = 0
Reorder the terms:
((40qr + 25q2) + -8r * (5q + 8r)) = 0
((40qr + 25q2) + -8r * (5q + 8r)) = 0
(40qr + 25q2 + (5q * -8r + 8r * -8r)) = 0
(40qr + 25q2 + (-40qr + -64r2)) = 0
Reorder the terms:
(40qr + -40qr + 25q2 + -64r2) = 0
Combine like terms: 40qr + -40qr = 0
(0 + 25q2 + -64r2) = 0
(25q2 + -64r2) = 0
Solving
25q2 + -64r2 = 0
Solving for variable 'q'.
Move all terms containing q to the left, all other terms to the right.
Add '64r2' to each side of the equation.
25q2 + -64r2 + 64r2 = 0 + 64r2
Combine like terms: -64r2 + 64r2 = 0
25q2 + 0 = 0 + 64r2
25q2 = 0 + 64r2
Remove the zero:
25q2 = 64r2
Divide each side by '25'.
q2 = 2.56r2
Simplifying
q2 = 2.56r2
Take the square root of each side:
q = {-1.6r, 1.6r}
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