Answer:
x = -2
x= -3
Explanation:
x 2+5x+6=0
To solve the equation, factor x^2+5x+6 using formula x^2+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=5
ab=6
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 6.
1,6
2,3
Calculate the sum for each pair.
1+6=7
2+3=5
The solution is the pair that gives sum 5.
a=2
b=3
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x+2)(x+3)
To find equation solutions, solve x+2=0 and x+3=0.
x=−2
x=−3