**The Quadratic Formula**

Part 2

Part 2

Yesterday we began discussing the quadratic formula, and I asked you to solve a specific quadratic equation using the formula. You can see that post here: Solving Quadratic Equations with the Quadratic Formula

Today I will provide the solution to that problem. For your reference, let me give you the quadratic formula one more time:

The solutions to the quadratic equation ** ax^{2} + bx + c = 0 **are

**Example:** Solve the quadratic equation *x*^{2} – 2*x – *15* = *0 by using the quadratic formula.

**Solution:**

So, the two solutions are 1 + 4 = **5**, and 1 – 4 = **–3**

**Note: **This particular problem could be solved more easily by factoring.

Why does the quadratic formula look so messy? It’s not a very pleasant looking formula. It would have been nicer if we had a simpler formula for solving a quadratic equation. But unfortunately, this is simply what it turned out to be. As a challenging exercise, I would like you to see this for yourself firsthand. I will give a full solution tomorrow:

**Challenge Problem: **Solve the general quadratic equation *ax*^{2} + *bx *+ *c* = 0 by completing the square, and note that this gives a derivation of the quadratic formula.

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