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Simplifying
(2q + 5r)(2q + -5r) = 0
Multiply (2q + 5r) * (2q + -5r)
(2q * (2q + -5r) + 5r * (2q + -5r)) = 0
((2q * 2q + -5r * 2q) + 5r * (2q + -5r)) = 0
Reorder the terms:
((-10qr + 4q2) + 5r * (2q + -5r)) = 0
((-10qr + 4q2) + 5r * (2q + -5r)) = 0
(-10qr + 4q2 + (2q * 5r + -5r * 5r)) = 0
(-10qr + 4q2 + (10qr + -25r2)) = 0
Reorder the terms:
(-10qr + 10qr + 4q2 + -25r2) = 0
Combine like terms: -10qr + 10qr = 0
(0 + 4q2 + -25r2) = 0
(4q2 + -25r2) = 0
Solving
4q2 + -25r2 = 0
Solving for variable 'q'.
Move all terms containing q to the left, all other terms to the right.
Add '25r2' to each side of the equation.
4q2 + -25r2 + 25r2 = 0 + 25r2
Combine like terms: -25r2 + 25r2 = 0
4q2 + 0 = 0 + 25r2
4q2 = 0 + 25r2
Remove the zero:
4q2 = 25r2
Divide each side by '4'.
q2 = 6.25r2
Simplifying
q2 = 6.25r2
Take the square root of each side:
q = {-2.5r, 2.5r}
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