HELP PLEASEE! Can anyone solve this?

Notice that the constant term in the quadratic is positive. That means the constant term in the two factors must both be positive or both be negative. Notice that the coefficient of the x term is negative. That can only be possible if at least one of the constants in the factors is negative. So now we know both constants are negative. And since the constant term is 1, then both constant terms in the factors must be -1.

So we know that the factors must have the form:

(ax - 1)(bx - 1)

multiplying this out we can see that a*b = 6 and (-a - b) = -4 AND we are stuck. There are no rational solutions for this. Now that we know there are no rational solutions we can consider other methods. We can always use the method of completing the square but since the coefficient of x^2 isn't itself a square that doesn't look like a very promising approach. The final fall-back approach is to use the quadratic formula. You may remember that the quadratic formula is derived by completing the square, so in a sense we ARE using the completing a square method.

a = 6

b = -4

c = 1

x = [-b ±√(b^2-4ac)]/2a

Now look at the discriminant, b^2-4ac = 16 -4(6) = -12. So we have to take the square root of a negative value to solve the equation. We cannot do that and still have a real result. So the solutions to the problem must be complex.

x = [4 ±i√12]/12 = 1/3 ±i√3/6]