x2+13x+42=0
Two solutions were found :
x = -6 x = -7Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring x2+13x+42
The first term is, x2 its coefficient is 1 .
The middle term is, +13x its coefficient is 13 .
The last term, "the constant", is +42
Step-1 : Multiply the coefficient of the first term by the constant 1 • 42 = 42
Step-2 : Find two factors of 42 whose sum equals the coefficient of the middle term, which is 13 .
| -42 | + | -1 | = | -43 | ||
| -21 | + | -2 | = | -23 | ||
| -14 | + | -3 | = | -17 | ||
| -7 | + | -6 | = | -13 | ||
| -6 | + | -7 | = | -13 | ||
| -3 | + | -14 | = | -17 | ||
| -2 | + | -21 | = | -23 | ||
| -1 | + | -42 | = | -43 | ||
| 1 | + | 42 | = | 43 | ||
| 2 | + | 21 | = | 23 | ||
| 3 | + | 14 | = | 17 | ||
| 6 | + | 7 | = | 13 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 7
x2 + 6x + 7x + 42
Step-4 : Add up the first 2 terms, pulling out factors :
x • (x+6)
Add up the last 2 terms, pulling out common factors :
7 • (x+6)
Step-5 : Add up the four terms of step 4 :
(x+7) • (x+6)
Which is the desired factorization
Equation at the end of step 1 :
(x + 7) • (x + 6) = 0
