Step-by-step explanation:
To solve the equation, factor x
2
+x−56 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=1
ab=−56
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −56.
−1,56
−2,28
−4,14
−7,8
Calculate the sum for each pair
−1+56=55
−2+28=26
−4+14=10
−7+8=1
The solution is the pair that gives sum 1.
a=−7
b=8
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x−7)(x+8)
To find equation solutions, solve x−7=0 and x+8=0.
x=7
x=−8
