Solve 1/2mx^2=0

$$\frac { 1 } { 2 } m x ^ { 2 } = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{x^{2}}{2}m=0$$

Divide 0 by \frac{1}{2}x^{2}.

$$m=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&m=0\end{matrix}\right.$$

Steps by Finding Square Root

Dividing by \frac{1}{2}m undoes the multiplication by \frac{1}{2}m.

$$x^{2}=\frac{0\times 2}{m}$$

Divide 0 by \frac{1}{2}m.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{m}{2}x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2}m for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2\times \frac{m}{2}}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2\times \frac{m}{2}}$$

Multiply 2 times \frac{1}{2}m.

$$x=\frac{0}{m}$$

Divide 0 by m.

$$x=0$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{x^{2}}{2}m=0$$

Divide 0 by \frac{1}{2}x^{2}.

$$m=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$