Example 7: Solve the following equations by factoring. 1 9x^2-6x+1=0 2. x^2+x-12=0 9x^2-6x+1=(3x-1)^2

Let's solve the given equations by factoring.1. To solve this equation by factoring, we need to find two numbers whose product is equal to the product of the coefficient of (which is 9) and the constant term (which is 1), and whose sum is equal to the coefficient of (which is -6).The two numbers that satisfy these conditions are -3 and -1. Therefore, we can rewrite the equation as: Now, we can set each factor equal to zero and solve for : Solving for , we get: So, the solution to the equation is .2. To solve this equation by factoring, we need to find two numbers whose product is equal to the product of the coefficient of (which is 1) and the constant term (which is -12), and whose sum is equal to the coefficient of (which is 1).The two numbers that satisfy these conditions are 4 and -3. Therefore, we can rewrite the equation as: Now, we can set each factor equal to zero and solve for : or Solving for , we get: or So, the solutions to the equation are and .