Solve (a-1)sqrt{x}=0

$$( a - 1 ) \sqrt { x } = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}\\a=1\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-1 by \sqrt{x}.

$$a\sqrt{x}-\sqrt{x}=0$$

Add \sqrt{x} to both sides. Anything plus zero gives itself.

$$a\sqrt{x}=\sqrt{x}$$

The equation is in standard form.

$$\sqrt{x}a=\sqrt{x}$$

Divide both sides by \sqrt{x}.

$$\frac{\sqrt{x}a}{\sqrt{x}}=\frac{\sqrt{x}}{\sqrt{x}}$$

Dividing by \sqrt{x} undoes the multiplication by \sqrt{x}.

$$a=\frac{\sqrt{x}}{\sqrt{x}}$$

Divide \sqrt{x} by \sqrt{x}.

$$a=1$$

Solve for a

$$\left\{\begin{matrix}a=1\text{, }&x\geq 0\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-1 by \sqrt{x}.

$$a\sqrt{x}-\sqrt{x}=0$$

Add \sqrt{x} to both sides. Anything plus zero gives itself.

$$a\sqrt{x}=\sqrt{x}$$

The equation is in standard form.

$$\sqrt{x}a=\sqrt{x}$$

Divide both sides by \sqrt{x}.

$$\frac{\sqrt{x}a}{\sqrt{x}}=\frac{\sqrt{x}}{\sqrt{x}}$$

Dividing by \sqrt{x} undoes the multiplication by \sqrt{x}.

$$a=\frac{\sqrt{x}}{\sqrt{x}}$$

Divide \sqrt{x} by \sqrt{x}.

$$a=1$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\geq 0\text{, }&a=1\end{matrix}\right.$$

Steps for Solving Radical Equations

Divide both sides by a-1.

$$\frac{\left(a-1\right)\sqrt{x}}{a-1}=\frac{0}{a-1}$$

Dividing by a-1 undoes the multiplication by a-1.

$$\sqrt{x}=\frac{0}{a-1}$$

Divide 0 by a-1.

$$\sqrt{x}=0$$

Square both sides of the equation.

$$x=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&a=1\end{matrix}\right.$$