The Quadratic Formula

The quadratic formula enables you to solve any equation of the form ax2 + 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.
x2 + x - 2 = 0

Solution
Based on ax2 + 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.
-x2 + 4x + 9 = 0
Solution
Based on ax2 + 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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