Basic Math Examples

${(2 a - 1)}^{2} = 39$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$2 a - 1 = \pm \sqrt{39}$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$2 a - 1 = \sqrt{39}$

Step 2.2

Add $1$ to both sides of the equation.

$2 a = \sqrt{39} + 1$

Step 2.3

Divide each term in $2 a = \sqrt{39} + 1$ by $2$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $2 a = \sqrt{39} + 1$ by $2$ .

$\frac{2 a}{2} = \frac{\sqrt{39}}{2} + \frac{1}{2}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{\sqrt{39}}{2} + \frac{1}{2}$

Step 2.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{\sqrt{39}}{2} + \frac{1}{2}$

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$2 a - 1 = - \sqrt{39}$

Step 2.5

Add $1$ to both sides of the equation.

$2 a = - \sqrt{39} + 1$

Step 2.6

Divide each term in $2 a = - \sqrt{39} + 1$ by $2$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in $2 a = - \sqrt{39} + 1$ by $2$ .

$\frac{2 a}{2} = \frac{- \sqrt{39}}{2} + \frac{1}{2}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.6.2.1.1

Cancel the common factor.

$\frac{2 a}{2} = \frac{- \sqrt{39}}{2} + \frac{1}{2}$

Step 2.6.2.1.2

Divide $a$ by $1$ .

$a = \frac{- \sqrt{39}}{2} + \frac{1}{2}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Move the negative in front of the fraction.

$a = - \frac{\sqrt{39}}{2} + \frac{1}{2}$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$a = \frac{\sqrt{39}}{2} + \frac{1}{2}, - \frac{\sqrt{39}}{2} + \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{\sqrt{39}}{2} + \frac{1}{2}, - \frac{\sqrt{39}}{2} + \frac{1}{2}$

Decimal Form:

$a = 3.62249899 \dots, - 2.62249899 \dots$