Algebra Examples

$\frac{4}{9} x^{2} - \frac{4}{3} x = - 1$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{4}{9}$ and $x^{2}$ .

$\frac{4 x^{2}}{9} - \frac{4}{3} x = - 1$

Step 1.2

Combine $x$ and $\frac{4}{3}$ .

$\frac{4 x^{2}}{9} - \frac{x \cdot 4}{3} = - 1$

Step 1.3

Move $4$ to the left of $x$ .

$\frac{4 x^{2}}{9} - \frac{4 x}{3} = - 1$

Step 2

Multiply each term in $\frac{4 x^{2}}{9} - \frac{4 x}{3} = - 1$ by $9$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $\frac{4 x^{2}}{9} - \frac{4 x}{3} = - 1$ by $9$ .

$\frac{4 x^{2}}{9} \cdot 9 - \frac{4 x}{3} \cdot 9 = - 1 \cdot 9$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 2.2.1.1.1

Cancel the common factor.

$\frac{4 x^{2}}{9} \cdot 9 - \frac{4 x}{3} \cdot 9 = - 1 \cdot 9$

Step 2.2.1.1.2

Rewrite the expression.

$4 x^{2} - \frac{4 x}{3} \cdot 9 = - 1 \cdot 9$

Step 2.2.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.2.1

Move the leading negative in $- \frac{4 x}{3}$ into the numerator.

$4 x^{2} + \frac{- 4 x}{3} \cdot 9 = - 1 \cdot 9$

Step 2.2.1.2.2

Factor $3$ out of $9$ .

$4 x^{2} + \frac{- 4 x}{3} \cdot (3 (3)) = - 1 \cdot 9$

Step 2.2.1.2.3

Cancel the common factor.

$4 x^{2} + \frac{- 4 x}{3} \cdot (3 \cdot 3) = - 1 \cdot 9$

Step 2.2.1.2.4

Rewrite the expression.

$4 x^{2} - 4 x \cdot 3 = - 1 \cdot 9$

Step 2.2.1.3

Multiply $3$ by $- 4$ .

$4 x^{2} - 12 x = - 1 \cdot 9$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Multiply $- 1$ by $9$ .

$4 x^{2} - 12 x = - 9$

Step 3

Add $9$ to both sides of the equation.

$4 x^{2} - 12 x + 9 = 0$

Step 4

Factor using the perfect square rule.

Tap for more steps...

Step 4.1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

${(2 x)}^{2} - 12 x + 9 = 0$

Step 4.2

Rewrite $9$ as $3^{2}$ .

${(2 x)}^{2} - 12 x + 3^{2} = 0$

Step 4.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot (2 x) \cdot 3$

Step 4.4

Rewrite the polynomial.

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

Step 4.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 x$ and $b = 3$ .

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

Step 5

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

$2 x - 3 = 0$

Step 6

Solve for $x$ .

Tap for more steps...

Step 6.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

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

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

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

Step 6.2.2.1.2

Divide $x$ by $1$ .

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$