Trigonometry Examples

$4 - \sqrt{2 x - 5} = 1$

Step 1

Move all terms not containing $- \sqrt{2 x - 5}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $4$ from both sides of the equation.

$- \sqrt{2 x - 5} = 1 - 4$

Step 1.2

Subtract $4$ from $1$ .

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

Step 2

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

${(- \sqrt{2 x - 5})}^{2} = {(- 3)}^{2}$

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 $\sqrt{2 x - 5}$ as ${(2 x - 5)}^{\frac{1}{2}}$ .

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

Apply the product rule to $- {(2 x - 5)}^{\frac{1}{2}}$ .

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

Step 3.2.1.2

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

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

Step 3.2.1.3

Multiply ${({(2 x - 5)}^{\frac{1}{2}})}^{2}$ by $1$ .

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

Step 3.2.1.4

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

Tap for more steps...

Step 3.2.1.4.1

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

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

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.

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

Step 3.2.1.4.2.2

Rewrite the expression.

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

Step 3.2.1.5

Simplify.

$2 x - 5 = {(- 3)}^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise $- 3$ to the power of $2$ .

$2 x - 5 = 9$

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

Add $5$ to both sides of the equation.

$2 x = 9 + 5$

Step 4.1.2

Add $9$ and $5$ .

$2 x = 14$

Step 4.2

Divide each term in $2 x = 14$ by $2$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $14$ by $2$ .

$x = 7$