If the discriminant $\Delta$ of the quadratic equation $ax^2 + bx + c = 0$ is exactly equal to $b^2$, which of the following is a necessary conclusion about the solutions of the equation?

Find the values of $k$ such that the equation $x^2 - kx + 9 = 0$ has exactly one real solution.

Find the exact solutions for the quadratic equation $2m^2-14m+23=0$ using the quadratic formula.

Fill in the blank: To solve $x^2 + 12x = 5$ by completing the square, you must add ________ to both sides of the equation to create a perfect square trinomial on the left side.

True or False: The quadratic formula can be used to solve the equation ${x^2 - 9 = 0}$ by substituting ${a = 1, b = 0,}$ and .