Question

solve for w.
$w^2 - 6w + 9 = 0$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$w = \square$

Explanation:

Step1: Factor the quadratic equation

The quadratic equation \(w^2 - 6w + 9 = 0\) can be factored as a perfect square trinomial. Recall that \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = w\) and \(2ab = 6w\), so \(b = 3\) (since \(2 \times w \times 3 = 6w\)). Thus, the equation factors to \((w - 3)^2 = 0\).

Step2: Solve for \(w\)

To solve \((w - 3)^2 = 0\), we take the square root of both sides. The square root of a square is the absolute value, but since the right side is 0, we have \(w - 3 = 0\) (because the square root of 0 is 0). Solving for \(w\), we add 3 to both sides: \(w = 3\). Since this is a repeated root (the square of a binomial equal to 0 gives a single solution with multiplicity 2), the solution is \(w = 3\).

Answer:

\(w = 3\)