Algebra Examples

$1 - \sqrt{3 x + 2} = - 5$

Step 1

Move all terms not containing $- \sqrt{3 x + 2}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $1$ from both sides of the equation.

$- \sqrt{3 x + 2} = - 5 - 1$

Step 1.2

Subtract $1$ from $- 5$ .

$- \sqrt{3 x + 2} = - 6$

Step 2

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

${(- \sqrt{3 x + 2})}^{2} = {(- 6)}^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

${(- {(3 x + 2)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

${(- 1)}^{2} {({(3 x + 2)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 3.2.1.2

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

$1 {({(3 x + 2)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 3.2.1.3

Multiply ${({(3 x + 2)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(3 x + 2)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 3.2.1.4

Multiply the exponents in ${({(3 x + 2)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.4.1

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

${(3 x + 2)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Step 3.2.1.4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.4.2.1

Cancel the common factor.

${(3 x + 2)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Step 3.2.1.4.2.2

Rewrite the expression.

${(3 x + 2)}^{1} = {(- 6)}^{2}$

Step 3.2.1.5

Simplify.

$3 x + 2 = {(- 6)}^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

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

$3 x + 2 = 36$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $2$ from both sides of the equation.

$3 x = 36 - 2$

Step 4.1.2

Subtract $2$ from $36$ .

$3 x = 34$

Step 4.2

Divide each term in $3 x = 34$ by $3$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $3 x = 34$ by $3$ .

$\frac{3 x}{3} = \frac{34}{3}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{34}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{34}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{34}{3}$

Decimal Form:

$x = 11.\overline{3}$

Mixed Number Form:

$x = 11 \frac{1}{3}$