Answer:
b = -9; b = -4
Explanation:
b^2 + 13b + 36 is in standard form, whose general equation is:
ax^2 + bx + c = 0.
Thus, 1 = a, 13 = b, and 36 = c.
To solve by factoring, we want to find two terms whose product equals a * c and whose sum equals b. Thus, we should list the factors of 1 and 36:
1 * 36 = 36
2 * 18 = 36
3 * 12 = 36
4 * 9 = 36
6 * 6 = 36
9 * 4 = 36 and 9 + 4 = 13
Thus, we have:
(b + 9)(b + 4) = 0
Now we set each term equal to 0 and solve for b:
Setting b + 9 equal to 0:
b + 9 = 0
b = -9
Setting b + 4 equal to 0:
b + 4 = 0
b = -4
Thus, the solutions to b^2 + 13b + 36 = 0 are b = -9 and b = -4.