To solve the quadratic equation x² − 6x + 9 = 0, we can factor it as a perfect square trinomial. Step 1: Factor the quadratic equation The equation x² − 6x + 9 is in the form a² − 2ab + b², which factors to (a−b)². Here, a=x and b=3. So, x² − 6x + 9 = (x−3)². Step 2: Set the factored expression to zero and solve for x (x−3)² = 0 Take the square root of both sides: √((x−3)²) = √(0); x−3 = 0 Add 3 to both sides: x = 3 The solution to the equation is: x=3

X²−6x+9=0

October 20, 2026Mathematics

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Answer

x=3

Step-by-step solution

2 steps

To solve the quadratic equation $x^2 - 6x + 9 = 0$ , we can factor it as a perfect square trinomial.

Factor the quadratic equation
The equation $x^2 - 6x + 9$ is in the form $a^2 - 2ab + b^2$ , which factors to $(a-b)^2$ .
Here, $a=x$ and $b=3$ .
So, $x^2 - 6x + 9 = (x-3)^2$ .
Set the factored expression to zero and solve for x
$(x-3)^2 = 0$
Take the square root of both sides:
$\sqrt{(x-3)^2} = \sqrt{0}$
$x-3 = 0$
Add 3 to both sides:
$x = 3$

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X²−6x+9=0

Answer

Step-by-step solution

Factor the quadratic equation

Set the factored expression to zero and solve for x

Try one yourself

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