# Completing the Square

There are more exercises available, and if you find yourself struggling, it’s a good idea to do them and keep track of which you are able to solve and which give you difficulty.

1. $\rhd$ Introduction to completing the square (14:06) How to solve equations such as $x^2-4x = 5$ and $10x^2 - 30x - 8 = 0$ by using the technique of completing the square.Be careful about answers that are irreducible radicals — be sure you give the exact, correct answer (the radical).  If requested, you can also give a decimal approximation, but remember that it is only an approximation.  If Sal had verified his results algebraically instead of with the calculator, he would have seen that the left hand is exactly, not approximately, zero when the solutions are substituted in for $x$.
2. $\rhd$ Rewriting quadratics as perfect squares (3:01) Rewrite $x^2 + 16x +9$ as $(x + 8)^2 - 55$.
3. $\star$ Rewriting quadratics as perfect squares   Examples such as $x^2 + 20x +40$.
4. $\rhd$ Solving quadratics by completing the square (6:18)
How to solve $x^2 - 2x - 8 = 0$ by rewriting it as $(x-1)^2 - 9 = 0$.
5. $\rhd$ Solving quadratics by completing the square when the leading coefficient is not 1 (5:43) Example: $4x^2 + 40x - 300 = 0$.