Graph x^2-18x+81<=0

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Graph x^2-18x+81<=0

$x^{2} - 18 x + 81 \leq 0$

Convert the inequality to an equation.

$x^{2} - 18 x + 81 = 0$

Factor using the perfect square rule.

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Rewrite $81$ as $9^{2}$ .

$x^{2} - 18 x + 9^{2} = 0$

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

$18 x = 2 \cdot x \cdot 9$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 9 + 9^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 9$ .

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

Set the $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

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