Solve for x x=3 square root of x

$x = 3 \sqrt{x}$

Step 1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 \sqrt{x} = x$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${(3 \sqrt{x})}^{2} = x^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(3 x^{\frac{1}{2}})}^{2} = x^{2}$

Simplify the left side.

Simplify ${(3 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $3 x^{\frac{1}{2}}$ .

$3^{2} {(x^{\frac{1}{2}})}^{2} = x^{2}$

Raise $3$ to the power of $2$ .

$9 {(x^{\frac{1}{2}})}^{2} = x^{2}$

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$9 x^{\frac{1}{2} \cdot 2} = x^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 x^{\frac{1}{2} \cdot 2} = x^{2}$

Rewrite the expression.

$9 x^{1} = x^{2}$

Simplify.

$9 x = x^{2}$

Step 4

Solve for $x$ .

Subtract $x^{2}$ from both sides of the equation.

$9 x - x^{2} = 0$

Factor the left side of the equation.

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$9 u - u^{2} = 0$

Factor $u$ out of $9 u - u^{2}$ .

Factor $u$ out of $9 u$ .

$u \cdot 9 - u^{2} = 0$

Factor $u$ out of $- u^{2}$ .

$u \cdot 9 + u (- u) = 0$

Factor $u$ out of $u \cdot 9 + u (- u)$ .

$u (9 - u) = 0$

Replace all occurrences of $u$ with $x$ .

$x (9 - x) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$9 - x = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $9 - x$ equal to $0$ and solve for $x$ .

Set $9 - x$ equal to $0$ .

$9 - x = 0$

Solve $9 - x = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$- x = - 9$

Divide each term in $- x = - 9$ by $- 1$ and simplify.

Divide each term in $- x = - 9$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 9}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x = 9$

The final solution is all the values that make $x (9 - x) = 0$ true.

$x = 0, 9$

Solve for x x=3 square root of x

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