Solve f(x)=2-3x^2x_{0}=1

$$f ( x ) = 2 - 3 x ^ { 2 } x _ { 0 } = 1$$

Solve for x_0

$$x_{0}=\frac{1}{3x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply -1 and 3 to get -3.

$$2-3x^{2}x_{0}=1$$

Subtract 2 from both sides.

$$-3x^{2}x_{0}=1-2$$

Subtract 2 from 1 to get -1.

$$-3x^{2}x_{0}=-1$$

The equation is in standard form.

$$\left(-3x^{2}\right)x_{0}=-1$$

Divide both sides by -3x^{2}.

$$\frac{\left(-3x^{2}\right)x_{0}}{-3x^{2}}=-\frac{1}{-3x^{2}}$$

Dividing by -3x^{2} undoes the multiplication by -3x^{2}.

$$x_{0}=-\frac{1}{-3x^{2}}$$

Divide -1 by -3x^{2}.

$$x_{0}=\frac{1}{3x^{2}}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}x_{0}^{-\frac{1}{2}}}{3}$$

$$x=\frac{\sqrt{3}x_{0}^{-\frac{1}{2}}}{3}\text{, }x_{0}\neq 0$$

Solve for x

$$x=\frac{\sqrt{\frac{3}{x_{0}}}}{3}$$

$$x=-\frac{\sqrt{\frac{3}{x_{0}}}}{3}\text{, }x_{0}>0$$