Solve -x^2+bx+c=0

$$- x ^ { 2 } + b x + c = 0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=x-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

$$bx+c=x^{2}$$

Subtract c from both sides.

$$bx=x^{2}-c$$

The equation is in standard form.

$$xb=x^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{x^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{x^{2}-c}{x}$$

Divide x^{2}-c by x.

$$b=x-\frac{c}{x}$$

Solve for b

$$\left\{\begin{matrix}b=x-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

$$bx+c=x^{2}$$

Subtract c from both sides.

$$bx=x^{2}-c$$

The equation is in standard form.

$$xb=x^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{x^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{x^{2}-c}{x}$$

Divide x^{2}-c by x.

$$b=x-\frac{c}{x}$$

Solve for c

$$c=-x\left(b-x\right)$$

Solution Steps

Add x^{2} to both sides. Anything plus zero gives itself.

$$bx+c=x^{2}$$

Subtract bx from both sides.

$$c=x^{2}-bx$$