Pre-Algebra Examples

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

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

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite

9 x^{2}

$9 x^{2}$ as

{(3 x)}^{2}

${(3 x)}^{2}$ .

{(3 x)}^{2} - 12 x + 4 = 0

${(3 x)}^{2} - 12 x + 4 = 0$

Step 1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 1.3

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

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

Step 1.4

Rewrite the polynomial.

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

Step 1.5

Factor using the perfect square trinomial rule

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

$a = 3 x$ and

$b = 2$ .

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

Step 2

Set the

$3 x - 2$ equal to

$0$ .

$3 x - 2 = 0$

Step 3

Solve for

$x$ .

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Step 3.1

Add

$2$ to both sides of the equation.

$3 x = 2$

Step 3.2

Divide each term in

$3 x = 2$ by

$3$ and simplify.

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Step 3.2.1

Divide each term in

$3 x = 2$ by

$3$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

$3$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide

$x$ by

$1$ .

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