Solve sqrt{3p-k/2}=5

$$\sqrt { \frac { 3 p - k } { 2 } } = 5$$

Solve for k

$$k=3p-50$$

Steps for Solving Radical Equations

Divide each term of 3p-k by 2 to get \frac{3}{2}p-\frac{1}{2}k.

$$\sqrt{\frac{3}{2}p-\frac{1}{2}k}=5$$

Square both sides of the equation.

$$-\frac{1}{2}k+\frac{3p}{2}=25$$

Subtract \frac{3}{2}p from both sides of the equation.

$$-\frac{1}{2}k+\frac{3p}{2}-\frac{3p}{2}=25-\frac{3p}{2}$$

Subtracting \frac{3}{2}p from itself leaves 0.

$$-\frac{1}{2}k=25-\frac{3p}{2}$$

Subtract \frac{3}{2}p from 25.

$$-\frac{1}{2}k=-\frac{3p}{2}+25$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}k}{-\frac{1}{2}}=\frac{-\frac{3p}{2}+25}{-\frac{1}{2}}$$

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

$$k=\frac{-\frac{3p}{2}+25}{-\frac{1}{2}}$$

Divide 25-\frac{3p}{2} by -\frac{1}{2} by multiplying 25-\frac{3p}{2} by the reciprocal of -\frac{1}{2}.

$$k=3p-50$$

Solve for p

$$p=\frac{k+50}{3}$$

Steps for Solving Radical Equations

Divide each term of 3p-k by 2 to get \frac{3}{2}p-\frac{1}{2}k.

$$\sqrt{\frac{3}{2}p-\frac{1}{2}k}=5$$

Square both sides of the equation.

$$\frac{3}{2}p-\frac{k}{2}=25$$

Subtract -\frac{1}{2}k from both sides of the equation.

$$\frac{3}{2}p-\frac{k}{2}-\left(-\frac{k}{2}\right)=25-\left(-\frac{k}{2}\right)$$

Subtracting -\frac{1}{2}k from itself leaves 0.

$$\frac{3}{2}p=25-\left(-\frac{k}{2}\right)$$

Subtract -\frac{1}{2}k from 25.

$$\frac{3}{2}p=\frac{k}{2}+25$$

Divide both sides of the equation by \frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{3}{2}p}{\frac{3}{2}}=\frac{\frac{k}{2}+25}{\frac{3}{2}}$$

Dividing by \frac{3}{2} undoes the multiplication by \frac{3}{2}.

$$p=\frac{\frac{k}{2}+25}{\frac{3}{2}}$$

Divide 25+\frac{k}{2} by \frac{3}{2} by multiplying 25+\frac{k}{2} by the reciprocal of \frac{3}{2}.

$$p=\frac{k+50}{3}$$