x2 + 2x- 168=0 find the answer by middleterm
Answers
Answer:
Factoring x2-2x-168
The first term is, x2 its coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -168
Step-1 : Multiply the coefficient of the first term by the constant 1 • -168 = -168
Step-2 : Find two factors of -168 whose sum equals the coefficient of the middle term, which is -2 .
-168 + 1 = -167
-84 + 2 = -82
-56 + 3 = -53
-42 + 4 = -38
-28 + 6 = -22
-24 + 7 = -17
-21 + 8 = -13
-14 + 12 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 12
x2 - 14x + 12x - 168
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-14)
Add up the last 2 terms, pulling out common factors :
12 • (x-14)
Step-5 : Add up the four terms of step 4 :
(x+12) • (x-14)
Which is the desired factorization
Equation at the end of step
1
:
(x + 12) • (x - 14) = 0
STEP
2
:
Theory - Roots of a product
Answer:
=>x²+2x-168=0
=>x²+(14-12)x-168=0
=>x²+14x-12x-168=0
=>x(x+14)-12(x+14)=0
=>(x+14)(x-12)=0
Either, or,
x+14=0 x-12=0
x= -14 x=12