Step 1: Identify the given equation. The equation is x² − 18x + 81 = 0. Step 2: Recognize the equation as a perfect square trinomial. A perfect square trinomial has the form a² − 2ab + b² = (a−b)². In this equation, a² = x² (so a=x), and b² = 81 (so b=9). The middle term is −18x, which matches −2ab = −2(x)(9) = −18x. Step 3: Factor the trinomial. Using the perfect square trinomial formula, we can rewrite the equation as (x−9)² = 0. Step 4: Solve for x. Take the square root of both sides: √((x−9)²) = √(0). This simplifies to x−9 = 0. Add 9 to both sides: x = 9. x² − 18x + 81 = 0; (x−9)² = 0; x−9 = 0; x = 9 The value of x is 9.

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August 18, 2026Mathematics

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Identify the given equation.
The equation is $x^2 - 18x + 81 = 0$ .
Recognize the equation as a perfect square trinomial.
A perfect square trinomial has the form $a^2 - 2ab + b^2 = (a-b)^2$ .
In this equation, $a^2 = x^2$ (so $a=x$ ), and $b^2 = 81$ (so $b=9$ ).
The middle term is $-18x$ , which matches $-2ab = -2(x)(9) = -18x$ .
Factor the trinomial.
Using the perfect square trinomial formula, we can rewrite the equation as $(x-9)^2 = 0$ .
Solve for x.
Take the square root of both sides: $\sqrt{(x-9)^2} = \sqrt{0}$ .
This simplifies to $x-9 = 0$ .
Add 9 to both sides: $x = 9$ .
$x^2 - 18x + 81 = 0$ $(x-9)^2 = 0$ $x-9 = 0$ $x = 9$
The value of x is 9.

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Help me to find x

Step-by-step solution

Identify the given equation.

Recognize the equation as a perfect square trinomial.

Factor the trinomial.

Solve for x.

Still stuck on this one?

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