Question

x² - 6x + 9 = 0

Explanation:

Step1: Identify the quadratic form

The equation is \(x^2 - 6x + 9 = 0\), which is a quadratic in the form \(ax^2+bx+c = 0\) with \(a = 1\), \(b=-6\), \(c = 9\). We can factor it or use the quadratic formula. Let's factor it. We need two numbers that multiply to \(9\) and add to \(-6\). Those numbers are \(-3\) and \(-3\).

Step2: Factor the quadratic

So, \(x^2 - 6x + 9=(x - 3)(x - 3)=0\) or \((x - 3)^2=0\).

Step3: Solve for \(x\)

Setting \((x - 3)^2 = 0\), we take the square root of both sides: \(x-3 = 0\), so \(x = 3\) (with multiplicity 2).

Answer:

\(x = 3\) (double root)