Consider the quadratic equation $x^{2} – 10x = –29$.

1. Is $x = 5 + 2i$ a solution to the equation? How can you be sure without solving?

   Step (a):

   Substitute the solution into the equation.

   $(5 + 2i)^2 - 10(5 + 2i) = -29$

2. Without solving, predict another solution to the equation. Verify your prediction by checking it.

   Hint (b):

   Any quadratic equation can be solved using the Quadratic Formula. The "$i$" part of the solution comes from a negative number inside of the square root. What is in front the the square root in the Quadratic Formula?

3. Where does the parabola $y = x^{2} – 10x + 29$ intersect the $x$-axis? Explain.

   Hint (c):

   Let $y = 0$ and solve.