Solve 2left(2xx+2x2x+2xxright)+18=2left(4x+x+xx+4xxright)

$$2 \left( 2xx+2x2x+2xx \right) +18 = 2 \left( 4x+x+xx+4xx \right)$$

Solve for x_2

$$x_{2}=\frac{x}{2}+\frac{5}{2}-\frac{9}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$2\left(2x^{2}+2x_{2}x+2xx\right)+18=2\left(4x+x+xx+4xx\right)$$

Multiply x and x to get x^{2}.

$$2\left(2x^{2}+2x_{2}x+2x^{2}\right)+18=2\left(4x+x+xx+4xx\right)$$

Multiply x and x to get x^{2}.

$$2\left(2x^{2}+2x_{2}x+2x^{2}\right)+18=2\left(4x+x+x^{2}+4xx\right)$$

Multiply x and x to get x^{2}.

$$2\left(2x^{2}+2x_{2}x+2x^{2}\right)+18=2\left(4x+x+x^{2}+4x^{2}\right)$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$2\left(4x^{2}+2x_{2}x\right)+18=2\left(4x+x+x^{2}+4x^{2}\right)$$

Use the distributive property to multiply 2 by 4x^{2}+2x_{2}x.

$$8x^{2}+4xx_{2}+18=2\left(4x+x+x^{2}+4x^{2}\right)$$

Combine 4x and x to get 5x.

$$8x^{2}+4xx_{2}+18=2\left(5x+x^{2}+4x^{2}\right)$$

Combine x^{2} and 4x^{2} to get 5x^{2}.

$$8x^{2}+4xx_{2}+18=2\left(5x+5x^{2}\right)$$

Use the distributive property to multiply 2 by 5x+5x^{2}.

$$8x^{2}+4xx_{2}+18=10x+10x^{2}$$

Subtract 8x^{2} from both sides.

$$4xx_{2}+18=10x+10x^{2}-8x^{2}$$

Combine 10x^{2} and -8x^{2} to get 2x^{2}.

$$4xx_{2}+18=10x+2x^{2}$$

Subtract 18 from both sides.

$$4xx_{2}=10x+2x^{2}-18$$

The equation is in standard form.

$$4xx_{2}=2x^{2}+10x-18$$

Divide both sides by 4x.

$$\frac{4xx_{2}}{4x}=\frac{2x^{2}+10x-18}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$x_{2}=\frac{2x^{2}+10x-18}{4x}$$

Divide 10x+2x^{2}-18 by 4x.

$$x_{2}=\frac{x}{2}+\frac{5}{2}-\frac{9}{2x}$$

Solve for x

$$x=-\frac{\sqrt{4x_{2}^{2}-20x_{2}+61}}{2}+x_{2}-\frac{5}{2}$$

$$x=\frac{\sqrt{4x_{2}^{2}-20x_{2}+61}}{2}+x_{2}-\frac{5}{2}$$