+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=−8
ab=−153
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −153.
1,−153
3,−51
9,−17
Calculate the sum for each pair.
1−153=−152
3−51=−48
9−17=−8
The solution is the pair that gives sum −8.
a=−17
b=9
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x−17)(x+9)
To find equation solutions, solve x−17=0 and x+9=0.
Answers & Comments
Answer:
x=17
x=−9
Step-by-step explanation:
STEPS USING FACTORING
(x−4) 2
=169
Use binomial theorem (a−b)
2
=a 2
−2ab+b 2 to expand (x−4)
2
.
x 2
−8x+16=169
Subtract 169 from both sides.
x
2
−8x+16−169=0
Subtract 169 from 16 to get −153.
x
2
−8x−153=0
To solve the equation, factor x
2
−8x−153 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=−8
ab=−153
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −153.
1,−153
3,−51
9,−17
Calculate the sum for each pair.
1−153=−152
3−51=−48
9−17=−8
The solution is the pair that gives sum −8.
a=−17
b=9
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x−17)(x+9)
To find equation solutions, solve x−17=0 and x+9=0.
x=17
x=−9
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