Algebra Examples

$\sqrt{2 b - 6} = \sqrt{3 b - 14}$

Step 1

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

${\sqrt{2 b - 6}}^{2} = {\sqrt{3 b - 14}}^{2}$

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 $\sqrt{2 b - 6}$ as ${(2 b - 6)}^{\frac{1}{2}}$ .

${({(2 b - 6)}^{\frac{1}{2}})}^{2} = {\sqrt{3 b - 14}}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(2 b - 6)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(2 b - 6)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

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

${(2 b - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 b - 14}}^{2}$

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.

${(2 b - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 b - 14}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 b - 6)}^{1} = {\sqrt{3 b - 14}}^{2}$

Step 2.2.1.2

Simplify.

$2 b - 6 = {\sqrt{3 b - 14}}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Rewrite ${\sqrt{3 b - 14}}^{2}$ as $3 b - 14$ .

Tap for more steps...

Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 b - 14}$ as ${(3 b - 14)}^{\frac{1}{2}}$ .

$2 b - 6 = {({(3 b - 14)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2

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

$2 b - 6 = {(3 b - 14)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.3

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

$2 b - 6 = {(3 b - 14)}^{\frac{2}{2}}$

Step 2.3.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.4.1

Cancel the common factor.

$2 b - 6 = {(3 b - 14)}^{\frac{2}{2}}$

Step 2.3.1.4.2

Rewrite the expression.

$2 b - 6 = {(3 b - 14)}^{1}$

Step 2.3.1.5

Simplify.

$2 b - 6 = 3 b - 14$

Step 3

Solve for $b$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $3 b$ from both sides of the equation.

$2 b - 6 - 3 b = - 14$

Step 3.1.2

Subtract $3 b$ from $2 b$ .

$- b - 6 = - 14$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $6$ to both sides of the equation.

$- b = - 14 + 6$

Step 3.2.2

Add $- 14$ and $6$ .

$- b = - 8$

Step 3.3

Divide each term in $- b = - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- b = - 8$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 8}{- 1}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 8}{- 1}$

Step 3.3.2.2

Divide $b$ by $1$ .

$b = \frac{- 8}{- 1}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $- 8$ by $- 1$ .

$b = 8$