Solve by Factoring -2 square root of 24x+13=-11

$- 2 \sqrt{24 x} + 13 = - 11$

Step 1

Add $11$ to both sides of the equation.

$- 2 \sqrt{24 x} + 13 + 11 = 0$

Step 2

Simplify $- 2 \sqrt{24 x} + 13 + 11$ .

Simplify each term.

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$- 2 \sqrt{4 (6) x} + 13 + 11 = 0$

Rewrite $4$ as $2^{2}$ .

$- 2 \sqrt{2^{2} \cdot 6 x} + 13 + 11 = 0$

Add parentheses.

$- 2 \sqrt{2^{2} \cdot (6 x)} + 13 + 11 = 0$

Pull terms out from under the radical.

$- 2 (2 \sqrt{6 x}) + 13 + 11 = 0$

Multiply $2$ by $- 2$ .

$- 4 \sqrt{6 x} + 13 + 11 = 0$

Add $13$ and $11$ .

$- 4 \sqrt{6 x} + 24 = 0$

Step 3

Factor $4$ out of $- 4 \sqrt{6 x} + 24$ .

Factor $4$ out of $- 4 \sqrt{6 x}$ .

$4 (- \sqrt{6 x}) + 24 = 0$

Factor $4$ out of $24$ .

$4 (- \sqrt{6 x}) + 4 (6) = 0$

Factor $4$ out of $4 (- \sqrt{6 x}) + 4 (6)$ .

$4 (- \sqrt{6 x} + 6) = 0$

Step 4

Divide each term in $4 (- \sqrt{6 x} + 6) = 0$ by $4$ and simplify.

Divide each term in $4 (- \sqrt{6 x} + 6) = 0$ by $4$ .

$\frac{4 (- \sqrt{6 x} + 6)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (- \sqrt{6 x} + 6)}{4} = \frac{0}{4}$

Divide $- \sqrt{6 x} + 6$ by $1$ .

$- \sqrt{6 x} + 6 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$- \sqrt{6 x} + 6 = 0$

Step 5

Subtract $6$ from both sides of the equation.

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

Step 6

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

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

Step 7

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $6 x$ .

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

Raise $- 1$ to the power of $2$ .

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

Multiply ${(6^{\frac{1}{2}})}^{2}$ by $1$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 6$ to the power of $2$ .

$6 x = 36$

Step 8

Divide each term in $6 x = 36$ by $6$ and simplify.

Divide each term in $6 x = 36$ by $6$ .

$\frac{6 x}{6} = \frac{36}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{36}{6}$

Divide $x$ by $1$ .

$x = \frac{36}{6}$

Simplify the right side.

Divide $36$ by $6$ .

$x = 6$

Solve by Factoring -2 square root of 24x+13=-11

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