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## The Quadratic Formula

The quadratic formula enables you to solve any equation of the form **ax**^{2} + bx + c = 0, even if the answers are not integers. If you are unable
to factor the trinomial, the quadratic formula is the best way to get the
answers.
The quadratic formula is:

The sample problems below will show you how the quadratic formula is used
to find the solutions of quadratic equations. The first problem is one that
you could also solve using factoring techniques. The second problem uses
a trinomial that you would not be able to easily factor.

**Problem 1**

Solve for x.

**x**^{2} + **x** - 2 = 0
**Solution**

Based on ax^{2} + bx + c, we have:

a = 1, b = 1, c = -2

Plugging into the quadratic formula results in these two answers:

Simplifying...

Final Answer:

x = 1, ^{- }2

**Problem 2**

Solve for x.

-**x**^{2} + 4**x** + 9 = 0

**Solution**

Based on ax^{2} + bx + c, we have:

a = -1, b = 4, c = 9
Plugging into the quadratic formula results in these two answers:

Simplifying...

Final Answer:

x = 2 - √13, 2 + √13

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