Solve 7x3x^2=0

$$7x3 { x }^{ 2 } =0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&x_{3}=0\end{matrix}\right.$$

Steps by Finding Square Root

Dividing by 7x_{3} undoes the multiplication by 7x_{3}.

$$x^{2}=\frac{0}{7x_{3}}$$

Divide 0 by 7x_{3}.

$$x^{2}=0$$

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.

$$7x_{3}x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7x_{3} for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2\times 7x_{3}}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2\times 7x_{3}}$$

Multiply 2 times 7x_{3}.

$$x=\frac{0}{14x_{3}}$$

Divide 0 by 14x_{3}.

$$x=0$$

Solve for x_3 (complex solution)

$$\left\{\begin{matrix}\\x_{3}=0\text{, }&\text{unconditionally}\\x_{3}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$7x^{2}x_{3}=0$$

Divide 0 by 7x^{2}.

$$x_{3}=0$$

Solve for x_3

$$\left\{\begin{matrix}\\x_{3}=0\text{, }&\text{unconditionally}\\x_{3}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$7x^{2}x_{3}=0$$

Divide 0 by 7x^{2}.

$$x_{3}=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&x_{3}=0\end{matrix}\right.$$