Example 7: Solve the following equations by factoring. 1 9x^2-6x+1=0

To solve the quadratic equation \(9x^2 - 6x + 1 = 0\) by factoring, we first need to rewrite it in a form that can be factored. <br /><br />Notice that the quadratic can be written as a perfect square trinomial:<br />\[ 9x^2 - 6x + 1 = (3x - 1)^2 \]<br /><br />So, the equation becomes:<br />\[ (3x - 1)^2 = 0 \]<br /><br />To solve for \(x\), we take the square root of both sides:<br />\[ 3x - 1 = 0 \]<br /><br />Solving for \(x\):<br />\[ 3x = 1 \]<br />\[ x = \frac{1}{3} \]<br /><br />Therefore, the solution to the equation \(9x^2 - 6x + 1 = 0\) is:<br />\[ x = \frac{1}{3} \]