Precalculus Examples

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

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

Step 1

Set

x^{2} - 12 x + 36

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

0

$0$ .

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

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

Step 2

Solve for

x

$x$ .

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Step 2.1

Factor using the perfect square rule.

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Step 2.1.1

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

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

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

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

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

Step 2.1.3

Rewrite the polynomial.

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

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

Step 2.1.4

Factor using the perfect square trinomial rule

a^{2} - 2 a b + b^{2} = {(a - b)}^{2}

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

a = x

$a = x$ and

b = 6

$b = 6$ .

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

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

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

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

Step 2.2

Set the

x - 6

$x - 6$ equal to

0

$0$ .

x - 6 = 0

$x - 6 = 0$

Step 2.3

Add

6

$6$ to both sides of the equation.

x = 6

$x = 6$ (Multiplicity of

2

$2$ )

x = 6

$x = 6$ (Multiplicity of

2

$2$ )

Step 3

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