Answer:
q = (4r²-p)/5
Step-by-step explanation:
To solve for q, undo what has been done to it. The variable q has been multiplied by 5, added to p, the square root taken, and that divided by 2. We undo these operations in reverse order.
[tex]\dfrac{\sqrt{p+5q}}{2}=r\qquad\text{given}\\\\\sqrt{p+5q}=2r\qquad\text{multiply by 2}\\\\p+5q=4r^2\qquad\text{square}\\\\5q=4r^2-p\qquad\text{subtract p}\\\\\boxed{q=\dfrac{4r^2-p}{5}}\qquad\text{divide by 5}[/tex]
