Trigonometry Examples

$\sqrt{3 x + 5} = 6$

Step 1

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

${\sqrt{3 x + 5}}^{2} = 6^{2}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x + 5}$ as ${(3 x + 5)}^{\frac{1}{2}}$ .

${({(3 x + 5)}^{\frac{1}{2}})}^{2} = 6^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(3 x + 5)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(3 x + 5)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

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

${(3 x + 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

${(3 x + 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(3 x + 5)}^{1} = 6^{2}$

Step 2.2.1.2

Simplify.

$3 x + 5 = 6^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

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

$3 x + 5 = 36$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $5$ from both sides of the equation.

$3 x = 36 - 5$

Step 3.1.2

Subtract $5$ from $36$ .

$3 x = 31$

Step 3.2

Divide each term in $3 x = 31$ by $3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $3 x = 31$ by $3$ .

$\frac{3 x}{3} = \frac{31}{3}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{31}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{31}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{31}{3}$

Decimal Form:

$x = 10.\overline{3}$

Mixed Number Form:

$x = 10 \frac{1}{3}$