Precalculus Examples

$3 {(3 x - 1)}^{2} = 21$

Step 1

Divide each term in $3 {(3 x - 1)}^{2} = 21$ by $3$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $3 {(3 x - 1)}^{2} = 21$ by $3$ .

$\frac{3 {(3 x - 1)}^{2}}{3} = \frac{21}{3}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{3 {(3 x - 1)}^{2}}{3} = \frac{21}{3}$

Step 1.2.1.2

Divide ${(3 x - 1)}^{2}$ by $1$ .

${(3 x - 1)}^{2} = \frac{21}{3}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $21$ by $3$ .

${(3 x - 1)}^{2} = 7$

Step 2

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

$3 x - 1 = \pm \sqrt{7}$

Step 3

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

Tap for more steps...

Step 3.1

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

$3 x - 1 = \sqrt{7}$

Step 3.2

Add $1$ to both sides of the equation.

$3 x = \sqrt{7} + 1$

Step 3.3

Divide each term in $3 x = \sqrt{7} + 1$ by $3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $3 x = \sqrt{7} + 1$ by $3$ .

$\frac{3 x}{3} = \frac{\sqrt{7}}{3} + \frac{1}{3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\sqrt{7}}{3} + \frac{1}{3}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{7}}{3} + \frac{1}{3}$

Step 3.4

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

$3 x - 1 = - \sqrt{7}$

Step 3.5

Add $1$ to both sides of the equation.

$3 x = - \sqrt{7} + 1$

Step 3.6

Divide each term in $3 x = - \sqrt{7} + 1$ by $3$ and simplify.

Tap for more steps...

Step 3.6.1

Divide each term in $3 x = - \sqrt{7} + 1$ by $3$ .

$\frac{3 x}{3} = \frac{- \sqrt{7}}{3} + \frac{1}{3}$

Step 3.6.2

Simplify the left side.

Tap for more steps...

Step 3.6.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \sqrt{7}}{3} + \frac{1}{3}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{7}}{3} + \frac{1}{3}$

Step 3.6.3

Simplify the right side.

Tap for more steps...

Step 3.6.3.1

Move the negative in front of the fraction.

$x = - \frac{\sqrt{7}}{3} + \frac{1}{3}$

Step 3.7

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

$x = \frac{\sqrt{7}}{3} + \frac{1}{3}, - \frac{\sqrt{7}}{3} + \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{7}}{3} + \frac{1}{3}, - \frac{\sqrt{7}}{3} + \frac{1}{3}$

Decimal Form:

$x = 1.21525043 \dots, - 0.54858377 \dots$