Solve m*4=1/4(p-q)^2*4

$$m \times 4 = \frac { 1 } { 4 } ( p - q ) ^ { 2 } \times 4$$

Solve for m

$$m=\frac{\left(p-q\right)^{2}}{4}$$

Solution Steps

Cancel out 4 on both sides.

$$m=\frac{1}{4}\left(p-q\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-q\right)^{2}.

$$m=\frac{1}{4}\left(p^{2}-2pq+q^{2}\right)$$

Use the distributive property to multiply \frac{1}{4} by p^{2}-2pq+q^{2}.

$$m=\frac{1}{4}p^{2}-\frac{1}{2}pq+\frac{1}{4}q^{2}$$

Solve for p

$$p=q-2\sqrt{m}$$

$$p=q+2\sqrt{m}\text{, }m\geq 0$$