Solve (a-2)x^2=0

$$( a - 2 ) x ^ { 2 } = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=2\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2 by x^{2}.

$$ax^{2}-2x^{2}=0$$

Add 2x^{2} to both sides. Anything plus zero gives itself.

$$ax^{2}=2x^{2}$$

The equation is in standard form.

$$x^{2}a=2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{2x^{2}}{x^{2}}$$

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

$$a=\frac{2x^{2}}{x^{2}}$$

Divide 2x^{2} by x^{2}.

$$a=2$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=2\end{matrix}\right.$$

Steps by Finding Square Root

Dividing by a-2 undoes the multiplication by a-2.

$$x^{2}=\frac{0}{a-2}$$

Divide 0 by a-2.

$$x^{2}=0$$

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

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

$$x=\frac{0±\sqrt{0^{2}}}{2\left(a-2\right)}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2\left(a-2\right)}$$

Multiply 2 times a-2.

$$x=\frac{0}{2a-4}$$

Divide 0 by 2a-4.

$$x=0$$

Solve for a

$$\left\{\begin{matrix}\\a=2\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-2 by x^{2}.

$$ax^{2}-2x^{2}=0$$

Add 2x^{2} to both sides. Anything plus zero gives itself.

$$ax^{2}=2x^{2}$$

The equation is in standard form.

$$x^{2}a=2x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{2x^{2}}{x^{2}}$$

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

$$a=\frac{2x^{2}}{x^{2}}$$

Divide 2x^{2} by x^{2}.

$$a=2$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&a=2\end{matrix}\right.$$