Trigonometry Examples

$\sqrt{7 x + 53} - 11 = - 6$

Step 1

Move all terms not containing $\sqrt{7 x + 53}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $11$ to both sides of the equation.

$\sqrt{7 x + 53} = - 6 + 11$

Step 1.2

Add $- 6$ and $11$ .

$\sqrt{7 x + 53} = 5$

Step 2

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

${\sqrt{7 x + 53}}^{2} = 5^{2}$

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 $\sqrt{7 x + 53}$ as ${(7 x + 53)}^{\frac{1}{2}}$ .

${({(7 x + 53)}^{\frac{1}{2}})}^{2} = 5^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(7 x + 53)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({(7 x + 53)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1.1

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

${(7 x + 53)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(7 x + 53)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(7 x + 53)}^{1} = 5^{2}$

Step 3.2.1.2

Simplify.

$7 x + 53 = 5^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise $5$ to the power of $2$ .

$7 x + 53 = 25$

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 $53$ from both sides of the equation.

$7 x = 25 - 53$

Step 4.1.2

Subtract $53$ from $25$ .

$7 x = - 28$

Step 4.2

Divide each term in $7 x = - 28$ by $7$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $7 x = - 28$ by $7$ .

$\frac{7 x}{7} = \frac{- 28}{7}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 28}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 28}{7}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $- 28$ by $7$ .

$x = - 4$