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

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

Solve for p

$$p=-\sqrt{7}\left(q-8\right)+23$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$p+\sqrt{7}q=8\sqrt{7}+23$$

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

$$p+\sqrt{7}q-\sqrt{7}q=8\sqrt{7}+23-\sqrt{7}q$$

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

$$p=8\sqrt{7}+23-\sqrt{7}q$$

Subtract q\sqrt{7} from 23+8\sqrt{7}.

$$p=-\sqrt{7}q+8\sqrt{7}+23$$

Solve for q

$$q=-\frac{\sqrt{7}\left(p-8\sqrt{7}-23\right)}{7}$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$\sqrt{7}q+p=8\sqrt{7}+23$$

Subtract p from both sides of the equation.

$$\sqrt{7}q+p-p=8\sqrt{7}+23-p$$

Subtracting p from itself leaves 0.

$$\sqrt{7}q=8\sqrt{7}+23-p$$

Subtract p from 23+8\sqrt{7}.

$$\sqrt{7}q=-p+8\sqrt{7}+23$$

Divide both sides by \sqrt{7}.

$$\frac{\sqrt{7}q}{\sqrt{7}}=\frac{-p+8\sqrt{7}+23}{\sqrt{7}}$$

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

$$q=\frac{-p+8\sqrt{7}+23}{\sqrt{7}}$$

Divide 23+8\sqrt{7}-p by \sqrt{7}.

$$q=\frac{\sqrt{7}\left(-p+8\sqrt{7}+23\right)}{7}$$