Solve x^2-px+g=0

$$x ^ { 2 } - p x + g = 0$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=x+\frac{g}{x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&g=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-px+g=-x^{2}$$

Subtract g from both sides.

$$-px=-x^{2}-g$$

The equation is in standard form.

$$\left(-x\right)p=-x^{2}-g$$

Divide both sides by -x.

$$\frac{\left(-x\right)p}{-x}=\frac{-x^{2}-g}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$p=\frac{-x^{2}-g}{-x}$$

Divide -x^{2}-g by -x.

$$p=x+\frac{g}{x}$$

Solve for g

$$g=-x\left(x-p\right)$$

Solution Steps

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-px+g=-x^{2}$$

Add px to both sides.

$$g=-x^{2}+px$$

Solve for p

$$\left\{\begin{matrix}p=x+\frac{g}{x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&g=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-px+g=-x^{2}$$

Subtract g from both sides.

$$-px=-x^{2}-g$$

The equation is in standard form.

$$\left(-x\right)p=-x^{2}-g$$

Divide both sides by -x.

$$\frac{\left(-x\right)p}{-x}=\frac{-x^{2}-g}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$p=\frac{-x^{2}-g}{-x}$$

Divide -x^{2}-g by -x.

$$p=x+\frac{g}{x}$$