Finite Math Examples

$5 \sqrt{x} = \sqrt{15 x + 60}$

Step 1

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

${(5 \sqrt{x})}^{2} = {\sqrt{15 x + 60}}^{2}$

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 $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(5 x^{\frac{1}{2}})}^{2} = {\sqrt{15 x + 60}}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

$5^{2} {(x^{\frac{1}{2}})}^{2} = {\sqrt{15 x + 60}}^{2}$

Step 2.2.1.2

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

$25 {(x^{\frac{1}{2}})}^{2} = {\sqrt{15 x + 60}}^{2}$

Step 2.2.1.3

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

Tap for more steps...

Step 2.2.1.3.1

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

$25 x^{\frac{1}{2} \cdot 2} = {\sqrt{15 x + 60}}^{2}$

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.

$25 x^{\frac{1}{2} \cdot 2} = {\sqrt{15 x + 60}}^{2}$

Step 2.2.1.3.2.2

Rewrite the expression.

$25 x^{1} = {\sqrt{15 x + 60}}^{2}$

Step 2.2.1.4

Simplify.

$25 x = {\sqrt{15 x + 60}}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify ${\sqrt{15 x + 60}}^{2}$ .

Tap for more steps...

Step 2.3.1.1

Factor $15$ out of $15 x + 60$ .

Tap for more steps...

Step 2.3.1.1.1

Factor $15$ out of $15 x$ .

$25 x = {\sqrt{15 (x) + 60}}^{2}$

Step 2.3.1.1.2

Factor $15$ out of $60$ .

$25 x = {\sqrt{15 x + 15 \cdot 4}}^{2}$

Step 2.3.1.1.3

Factor $15$ out of $15 x + 15 \cdot 4$ .

$25 x = {\sqrt{15 (x + 4)}}^{2}$

Step 2.3.1.2

Rewrite ${\sqrt{15 (x + 4)}}^{2}$ as $15 (x + 4)$ .

Tap for more steps...

Step 2.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15 (x + 4)}$ as ${(15 (x + 4))}^{\frac{1}{2}}$ .

$25 x = {({(15 (x + 4))}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2.2

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

$25 x = {(15 (x + 4))}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$25 x = {(15 (x + 4))}^{\frac{2}{2}}$

Step 2.3.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.2.4.1

Cancel the common factor.

$25 x = {(15 (x + 4))}^{\frac{2}{2}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$25 x = {(15 (x + 4))}^{1}$

Step 2.3.1.2.5

Simplify.

$25 x = 15 (x + 4)$

Step 2.3.1.3

Apply the distributive property.

$25 x = 15 x + 15 \cdot 4$

Step 2.3.1.4

Multiply $15$ by $4$ .

$25 x = 15 x + 60$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $15 x$ from both sides of the equation.

$25 x - 15 x = 60$

Step 3.1.2

Subtract $15 x$ from $25 x$ .

$10 x = 60$

Step 3.2

Divide each term in $10 x = 60$ by $10$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $10 x = 60$ by $10$ .

$\frac{10 x}{10} = \frac{60}{10}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{60}{10}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{60}{10}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $60$ by $10$ .

$x = 6$

Step 4