Module 8: Lesson 2
Are You Ready?
- x2 + 7x = −12
Rewrite the equation so it equates to 0.
x2 + 7x + 12 = 0
Since the coefficient of x2 is 1, you will find two factors that multiply to the third term and add to the middle term. To find the numbers that multiply to 12 and add to 7, write the set of factors for 12 and see which set of factors has a sum of 7.
| Product of 12 |
Sum |
| 1 × 12 |
13 |
| 2 × 6 |
8 |
| 3 × 4 |
7 |
Since 3 × 4 = 12 and 3 + 4 = 7, these are the factors that you need.
The factors of the equation are
(x + 3)(x + 4) = 0
Equate each factor to 0 and solve.
x + 3 = 0, x + 4 = 0
x = −3, x = −4
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