Solve x^2*b^2=0

$$x ^ { 2 } \cdot b ^ { 2 } = 0$$

Solve for b (complex solution)

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

Steps by Finding Square Root

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

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

Divide 0 by x^{2}.

$$b^{2}=0$$

Take the square root of both sides of the equation.

$$b=0 b=0$$

The equation is now solved. Solutions are the same.

$$b=0$$

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.

$$x^{2}b^{2}=0$$

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

$$b=\frac{0±\sqrt{0^{2}}}{2x^{2}}$$

Take the square root of 0^{2}.

$$b=\frac{0±0}{2x^{2}}$$

Multiply 2 times x^{2}.

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

Divide 0 by 2x^{2}.

$$b=0$$

Solve for x (complex solution)

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

Steps by Finding Square Root

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

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

Divide 0 by b^{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

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.

$$b^{2}x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2b^{2}}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2b^{2}}$$

Multiply 2 times b^{2}.

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

Divide 0 by 2b^{2}.

$$x=0$$

Solve for b

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

Solve for x

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