Solving Radical Equation for p
To solve the equation involving the radical, we want to isolate p. Given the equation from the image:
\[
\sqrt{\frac{2p+1}{t}} = 3
\]
First, square both sides of the equation to eliminate the square root:
\[
\left( \sqrt{\frac{2p+1}{t}} \right)^2 = 3^2
\]
This simplifies to:
\[
\frac{2p+1}{t} = 9
\]
Next, multiply both sides by t to remove the denominator:
\[
2p+1 = 9t
\]
Subtract 1 from both sides to isolate the term with p:
\[
2p = 9t - 1
\]
Finally, divide both sides by 2 to solve for p:
\[
p = \frac{9t - 1}{2}
\]
Therefore, the value of p in terms of t is:
\[
p = \frac{9t - 1}{2}
\]
