Algebra Examples

$9 x^{2} - 4 = 0$

Step 1

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

${(3 x)}^{2} - 4 = 0$

Step 2

Rewrite $4$ as $2^{2}$ .

${(3 x)}^{2} - 2^{2} = 0$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 2$ .

$(3 x + 2) (3 x - 2) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$3 x + 2 = 0$

$3 x - 2 = 0$

Step 5

Set $3 x + 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $3 x + 2$ equal to $0$ .

$3 x + 2 = 0$

Step 5.2

Solve $3 x + 2 = 0$ for $x$ .

Tap for more steps...

Step 5.2.1

Subtract $2$ from both sides of the equation.

$3 x = - 2$

Step 5.2.2

Divide each term in $3 x = - 2$ by $3$ and simplify.

Tap for more steps...

Step 5.2.2.1

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 5.2.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 5.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Step 5.2.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 6

Set $3 x - 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $3 x - 2$ equal to $0$ .

$3 x - 2 = 0$

Step 6.2

Solve $3 x - 2 = 0$ for $x$ .

Tap for more steps...

Step 6.2.1

Add $2$ to both sides of the equation.

$3 x = 2$

Step 6.2.2

Divide each term in $3 x = 2$ by $3$ and simplify.

Tap for more steps...

Step 6.2.2.1

Divide each term in $3 x = 2$ by $3$ .

$\frac{3 x}{3} = \frac{2}{3}$

Step 6.2.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{2}{3}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{3}$

Step 7

The final solution is all the values that make $(3 x + 2) (3 x - 2) = 0$ true.

$x = - \frac{2}{3}, \frac{2}{3}$