Find the range of values of k for which the expression x^2 -4x + k will be positive for all real values of x. Hence state the range of values of x satisfying the inequality x^2 -4x + 7 > 0.

For the first part, this is what i did:
(-4)^2 - 4(k) > 0
k<4

but how do i do the second part ("hence...")????

I need more information son

To find the range of values of x satisfying the inequality x^2 -4x + 7 > 0, we can use the fact that the quadratic expression x^2 - 4x + 7 can be factored as (x - 2)^2 + 3.

Now, we know that for a quadratic expression to be positive, the value of its discriminant should be negative. The discriminant for this quadratic expression is given by (-4)^2 - 4(1)(7) = 16 - 28 = -12.

Since the discriminant is negative, it means that the quadratic expression (x - 2)^2 + 3 is always positive for all real values of x. Hence, the range of values of x satisfying the inequality x^2 -4x + 7 > 0 is the entire real number line, or (-∞, +∞).

Therefore, the range of values of x satisfying the given inequality is (-∞, +∞).