Precalculus Examples

$- 1 - 16 = {(4 \sqrt{3 x + 12})}^{2}$

Step 1

Simplify ${(4 \sqrt{3 x + 12})}^{2}$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 x + 12$ .

Tap for more steps...

Step 1.1.1

Factor $3$ out of $3 x$ .

$- 1 - 16 = {(4 \sqrt{3 (x) + 12})}^{2}$

Step 1.1.2

Factor $3$ out of $12$ .

$- 1 - 16 = {(4 \sqrt{3 x + 3 \cdot 4})}^{2}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot 4$ .

$- 1 - 16 = {(4 \sqrt{3 (x + 4)})}^{2}$

Step 1.2

Simplify the expression.

Tap for more steps...

Step 1.2.1

Apply the product rule to $4 \sqrt{3 (x + 4)}$ .

$- 1 - 16 = 4^{2} {\sqrt{3 (x + 4)}}^{2}$

Step 1.2.2

Raise $4$ to the power of $2$ .

$- 1 - 16 = 16 {\sqrt{3 (x + 4)}}^{2}$

Step 1.3

Rewrite ${\sqrt{3 (x + 4)}}^{2}$ as $3 (x + 4)$ .

Tap for more steps...

Step 1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 (x + 4)}$ as ${(3 (x + 4))}^{\frac{1}{2}}$ .

$- 1 - 16 = 16 {({(3 (x + 4))}^{\frac{1}{2}})}^{2}$

Step 1.3.2

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

$- 1 - 16 = 16 {(3 (x + 4))}^{\frac{1}{2} \cdot 2}$

Step 1.3.3

Combine $\frac{1}{2}$ and $2$ .

$- 1 - 16 = 16 {(3 (x + 4))}^{\frac{2}{2}}$

Step 1.3.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.4.1

Cancel the common factor.

$- 1 - 16 = 16 {(3 (x + 4))}^{\frac{2}{2}}$

Step 1.3.4.2

Rewrite the expression.

$- 1 - 16 = 16 {(3 (x + 4))}^{1}$

Step 1.3.5

Simplify.

$- 1 - 16 = 16 (3 (x + 4))$

Step 1.4

Apply the distributive property.

$- 1 - 16 = 16 (3 x + 3 \cdot 4)$

Step 1.5

Multiply $3$ by $4$ .

$- 1 - 16 = 16 (3 x + 12)$

Step 1.6

Apply the distributive property.

$- 1 - 16 = 16 (3 x) + 16 \cdot 12$

Step 1.7

Multiply.

Tap for more steps...

Step 1.7.1

Multiply $3$ by $16$ .

$- 1 - 16 = 48 x + 16 \cdot 12$

Step 1.7.2

Multiply $16$ by $12$ .

$- 1 - 16 = 48 x + 192$

Step 2

Rewrite the equation as $48 x + 192 = - 1 - 16$ .

$48 x + 192 = - 1 - 16$

Step 3

Subtract $16$ from $- 1$ .

$48 x + 192 = - 17$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 4.1

Subtract $192$ from both sides of the equation.

$48 x = - 17 - 192$

Step 4.2

Subtract $192$ from $- 17$ .

$48 x = - 209$

Step 5

Divide each term in $48 x = - 209$ by $48$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $48 x = - 209$ by $48$ .

$\frac{48 x}{48} = \frac{- 209}{48}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $48$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{48 x}{48} = \frac{- 209}{48}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 209}{48}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Move the negative in front of the fraction.

$x = - \frac{209}{48}$

Step 6

Exclude the solutions that do not make $- 1 - 16 = {(4 \sqrt{3 x + 12})}^{2}$ true.

$No solution$