Solve sqrt{p+qsqrt{7}}=9/4-sqrt{1}

$$\sqrt { p + q \sqrt { 7 } } = \frac { 9 } { 4 - \sqrt { 1 } }$$

Solve for p

$$p=-\sqrt{7}q+9$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$p+\sqrt{7}q=9$$

Subtract q\sqrt{7} from both sides of the equation.

$$p+\sqrt{7}q-\sqrt{7}q=9-\sqrt{7}q$$

Subtracting q\sqrt{7} from itself leaves 0.

$$p=9-\sqrt{7}q$$

Subtract q\sqrt{7} from 9.

$$p=-\sqrt{7}q+9$$

Solve for q

$$q=-\frac{\sqrt{7}\left(p-9\right)}{7}$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$\sqrt{7}q+p=9$$

Subtract p from both sides of the equation.

$$\sqrt{7}q+p-p=9-p$$

Subtracting p from itself leaves 0.

$$\sqrt{7}q=9-p$$

Divide both sides by \sqrt{7}.

$$\frac{\sqrt{7}q}{\sqrt{7}}=\frac{9-p}{\sqrt{7}}$$

Dividing by \sqrt{7} undoes the multiplication by \sqrt{7}.

$$q=\frac{9-p}{\sqrt{7}}$$

Divide 9-p by \sqrt{7}.

$$q=\frac{\sqrt{7}\left(9-p\right)}{7}$$