Precalculus Examples

$y = x^{2} - 12 x + 36$

Step 1

Set $x^{2} - 12 x + 36$ equal to $0$ .

$x^{2} - 12 x + 36 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor using the perfect square rule.

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Step 2.1.1

Rewrite $36$ as $6^{2}$ .

$x^{2} - 12 x + 6^{2} = 0$

Step 2.1.2

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

$12 x = 2 \cdot x \cdot 6$

Step 2.1.3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 6 + 6^{2} = 0$

Step 2.1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 6$ .

${(x - 6)}^{2} = 0$

Step 2.2

Set the $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 2.3

Add $6$ to both sides of the equation.

$x = 6$ (Multiplicity of $2$ )

Step 3

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