Solve f(x)=2x+1quadg(x)=5x^2+2x+1quad

$$f ( x ) = 2 x + 1 \quad g ( x ) = 5 x ^ { 2 } + 2 x + 1 \quad$$

Solve for g

$$g=5x+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$1gx=5x^{2}+2x+1-2x$$

Combine 2x and -2x to get 0.

$$1gx=5x^{2}+1$$

Reorder the terms.

$$gx=5x^{2}+1$$

The equation is in standard form.

$$xg=5x^{2}+1$$

Divide both sides by x.

$$\frac{xg}{x}=\frac{5x^{2}+1}{x}$$

Dividing by x undoes the multiplication by x.

$$g=\frac{5x^{2}+1}{x}$$

Divide 5x^{2}+1 by x.

$$g=5x+\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{g^{2}-20}+g}{10}$$

$$x=\frac{\sqrt{g^{2}-20}+g}{10}$$

Solve for x

$$x=\frac{-\sqrt{g^{2}-20}+g}{10}$$

$$x=\frac{\sqrt{g^{2}-20}+g}{10}\text{, }|g|\geq 2\sqrt{5}$$