Solve f(x)=2x-8quadyquadg(x)=x^2-2x+5

$$f ( x ) = 2 x - 8 \quad y \quad g ( x ) = x ^ { 2 } - 2 x + 5$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{-x^{2}+4x-5}{8xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{C}\text{, }&\left(x=2+i\text{ or }x=2-i\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$-8ygx=x^{2}-2x+5-2x$$

Combine -2x and -2x to get -4x.

$$-8ygx=x^{2}-4x+5$$

The equation is in standard form.

$$\left(-8xy\right)g=x^{2}-4x+5$$

Divide both sides by -8yx.

$$\frac{\left(-8xy\right)g}{-8xy}=\frac{x^{2}-4x+5}{-8xy}$$

Dividing by -8yx undoes the multiplication by -8yx.

$$g=\frac{x^{2}-4x+5}{-8xy}$$

Divide 5-4x+x^{2} by -8yx.

$$g=-\frac{x^{2}-4x+5}{8xy}$$

Solve for g

$$g=\frac{-x^{2}+4x-5}{8xy}$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$-8ygx=x^{2}-2x+5-2x$$

Combine -2x and -2x to get -4x.

$$-8ygx=x^{2}-4x+5$$

The equation is in standard form.

$$\left(-8xy\right)g=x^{2}-4x+5$$

Divide both sides by -8yx.

$$\frac{\left(-8xy\right)g}{-8xy}=\frac{x^{2}-4x+5}{-8xy}$$

Dividing by -8yx undoes the multiplication by -8yx.

$$g=\frac{x^{2}-4x+5}{-8xy}$$

Divide x^{2}-4x+5 by -8yx.

$$g=-\frac{x^{2}-4x+5}{8xy}$$

Solve for x (complex solution)

$$x=-\sqrt{-16gy+16\left(gy\right)^{2}-1}-4gy+2$$

$$x=\sqrt{-16gy+16\left(gy\right)^{2}-1}-4gy+2$$

Solve for x

$$x=-\sqrt{-16gy+16\left(gy\right)^{2}-1}-4gy+2$$

$$x=\sqrt{-16gy+16\left(gy\right)^{2}-1}-4gy+2\text{, }\left(y\geq \frac{8\sqrt{5}|g|+16g}{32g^{2}}\text{ or }y\leq -\frac{8\sqrt{5}|g|-16g}{32g^{2}}\right)\text{ and }g\neq 0$$