Algebra Examples

$4 x^{2} - 12 x + 11 = 2$

Step 1

Subtract $2$ from both sides of the equation.

$4 x^{2} - 12 x + 11 - 2 = 0$

Step 2

Subtract $2$ from $11$ .

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

Step 3

Factor using the perfect square rule.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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 3.4

Rewrite the polynomial.

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

Step 3.5

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 4

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

$2 x - 3 = 0$

Step 5

Solve for $x$ .

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Step 5.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $2$ .

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Step 5.2.2.1.1

Cancel the common factor.

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

Step 5.2.2.1.2

Divide $x$ by $1$ .

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

Step 6