Solve 16/2quad25-5p+p^2/4=2px

$$\frac { 16 } { 2 } \quad 25 - 5 p + \frac { p ^ { 2 } } { 4 } = 2 p x$$

Solve for x

$$x=\frac{p}{8}-\frac{5}{2}+\frac{100}{p}$$

$$p\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$32\times 25-20p+p^{2}=8px$$

Multiply 32 and 25 to get 800.

$$800-20p+p^{2}=8px$$

Swap sides so that all variable terms are on the left hand side.

$$8px=800-20p+p^{2}$$

The equation is in standard form.

$$8px=p^{2}-20p+800$$

Divide both sides by 8p.

$$\frac{8px}{8p}=\frac{p^{2}-20p+800}{8p}$$

Dividing by 8p undoes the multiplication by 8p.

$$x=\frac{p^{2}-20p+800}{8p}$$

Divide 800-20p+p^{2} by 8p.

$$x=\frac{p}{8}-\frac{5}{2}+\frac{100}{p}$$

Solve for p (complex solution)

$$p=2\sqrt{4x^{2}+20x-175}+4x+10$$

$$p=-2\sqrt{4x^{2}+20x-175}+4x+10$$

Solve for p

$$p=2\sqrt{4x^{2}+20x-175}+4x+10$$

$$p=-2\sqrt{4x^{2}+20x-175}+4x+10\text{, }x\geq 5\sqrt{2}-\frac{5}{2}\text{ or }x\leq -5\sqrt{2}-\frac{5}{2}$$