Algebra Examples

$- 10 \sqrt{v - 10} = - 60$

Step 1

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

${(- 10 \sqrt{v - 10})}^{2} = {(- 60)}^{2}$

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 $\sqrt{v - 10}$ as ${(v - 10)}^{\frac{1}{2}}$ .

${(- 10 {(v - 10)}^{\frac{1}{2}})}^{2} = {(- 60)}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${(- 10 {(v - 10)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Apply the product rule to $- 10 {(v - 10)}^{\frac{1}{2}}$ .

${(- 10)}^{2} {({(v - 10)}^{\frac{1}{2}})}^{2} = {(- 60)}^{2}$

Step 2.2.1.2

Raise $- 10$ to the power of $2$ .

$100 {({(v - 10)}^{\frac{1}{2}})}^{2} = {(- 60)}^{2}$

Step 2.2.1.3

Multiply the exponents in ${({(v - 10)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.3.1

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

$100 {(v - 10)}^{\frac{1}{2} \cdot 2} = {(- 60)}^{2}$

Step 2.2.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.3.2.1

Cancel the common factor.

$100 {(v - 10)}^{\frac{1}{2} \cdot 2} = {(- 60)}^{2}$

Step 2.2.1.3.2.2

Rewrite the expression.

$100 {(v - 10)}^{1} = {(- 60)}^{2}$

Step 2.2.1.4

Simplify.

$100 (v - 10) = {(- 60)}^{2}$

Step 2.2.1.5

Apply the distributive property.

$100 v + 100 \cdot - 10 = {(- 60)}^{2}$

Step 2.2.1.6

Multiply $100$ by $- 10$ .

$100 v - 1000 = {(- 60)}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Raise $- 60$ to the power of $2$ .

$100 v - 1000 = 3600$

Step 3

Solve for $v$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $1000$ to both sides of the equation.

$100 v = 3600 + 1000$

Step 3.1.2

Add $3600$ and $1000$ .

$100 v = 4600$

Step 3.2

Divide each term in $100 v = 4600$ by $100$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $100 v = 4600$ by $100$ .

$\frac{100 v}{100} = \frac{4600}{100}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $100$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{100 v}{100} = \frac{4600}{100}$

Step 3.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{4600}{100}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $4600$ by $100$ .

$v = 46$