Solve for x x=2 square root of 6x-36

$x = 2 \sqrt{6 x - 36}$

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.

$2 \sqrt{6 x - 36} = x$

Step 2

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

${(2 \sqrt{6 x - 36})}^{2} = x^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x - 36}$ as ${(6 x - 36)}^{\frac{1}{2}}$ .

${(2 {(6 x - 36)}^{\frac{1}{2}})}^{2} = x^{2}$

Simplify the left side.

Simplify ${(2 {(6 x - 36)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $2 {(6 x - 36)}^{\frac{1}{2}}$ .

$2^{2} {({(6 x - 36)}^{\frac{1}{2}})}^{2} = x^{2}$

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

$4 {({(6 x - 36)}^{\frac{1}{2}})}^{2} = x^{2}$

Multiply the exponents in ${({(6 x - 36)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(6 x - 36)}^{\frac{1}{2} \cdot 2} = x^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(6 x - 36)}^{\frac{1}{2} \cdot 2} = x^{2}$

Rewrite the expression.

$4 {(6 x - 36)}^{1} = x^{2}$

Simplify.

$4 (6 x - 36) = x^{2}$

Apply the distributive property.

$4 (6 x) + 4 \cdot - 36 = x^{2}$

Multiply.

Multiply $6$ by $4$ .

$24 x + 4 \cdot - 36 = x^{2}$

Multiply $4$ by $- 36$ .

$24 x - 144 = x^{2}$

Step 4

Solve for $x$ .

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

$24 x - 144 - x^{2} = 0$

Factor the left side of the equation.

Factor $- 1$ out of $24 x - 144 - x^{2}$ .

Reorder the expression.

Move $- 144$ .

$24 x - x^{2} - 144 = 0$

Reorder $24 x$ and $- x^{2}$ .

$- x^{2} + 24 x - 144 = 0$

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 24 x - 144 = 0$

Factor $- 1$ out of $24 x$ .

$- (x^{2}) - (- 24 x) - 144 = 0$

Rewrite $- 144$ as $- 1 (144)$ .

$- (x^{2}) - (- 24 x) - 1 \cdot 144 = 0$

Factor $- 1$ out of $- (x^{2}) - (- 24 x)$ .

$- (x^{2} - 24 x) - 1 \cdot 144 = 0$

Factor $- 1$ out of $- (x^{2} - 24 x) - 1 (144)$ .

$- (x^{2} - 24 x + 144) = 0$

Factor using the perfect square rule.

Rewrite $144$ as $12^{2}$ .

$- (x^{2} - 24 x + 12^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$24 x = 2 \cdot x \cdot 12$

Rewrite the polynomial.

$- (x^{2} - 2 \cdot x \cdot 12 + 12^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 12$ .

$- {(x - 12)}^{2} = 0$

Divide each term in $- {(x - 12)}^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- {(x - 12)}^{2} = 0$ by $- 1$ .

$\frac{- {(x - 12)}^{2}}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{{(x - 12)}^{2}}{1} = \frac{0}{- 1}$

Divide ${(x - 12)}^{2}$ by $1$ .

${(x - 12)}^{2} = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

${(x - 12)}^{2} = 0$

Set the $x - 12$ equal to $0$ .

$x - 12 = 0$

Add $12$ to both sides of the equation.

$x = 12$

Solve for x x=2 square root of 6x-36

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