-17x2 - 14x + 10
 ————————————————
    2    Â
Step-by-step explanation:
STEP
1
:
      25
Simplify  ——
      2
Equation at the end of step
1
:
       25
 (((4•(x2))-(——•x2))-7x)+5
       2
STEP
2
:
Equation at the end of step 2
         25x2      Â
 (((4 • (x2)) -  ————) -  7x) +  5
         2       Â
STEP
3
:
Equation at the end of step
3
:
      25x2      Â
 ((22x2 -  ————) -  7x) +  5
      2       Â
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Â Subtracting a fraction from a whole
Rewrite the whole as a fraction using  2  as the denominator :
      22x2   22x2 • 2
  22x2 =  ————  =  ————————
       1      2  Â
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 Â Â Â Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
22x2 • 2 - (25x2)    -17x2
—————————————————  =  —————
    2        2 Â
Equation at the end of step
4
:
 -17x2     Â
 (————— -  7x) +  5
  2      Â
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Â Subtracting a whole from a fraction
Rewrite the whole as a fraction using  2  as the denominator :
     7x   7x • 2
  7x =  ——  =  ——————
     1     2 Â
Adding fractions that have a common denominator :
5.2 Â Â Â Adding up the two equivalent fractions
-17x2 - (7x • 2)   -17x2 - 14x
————————————————  =  ———————————
    2          2  Â
Equation at the end of step
5
:
 (-17x2 - 14x)  Â
 ————————————— +  5
    2     Â
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
6.1 Â Adding a whole to a fraction
Rewrite the whole as a fraction using  2  as the denominator :
    5   5 • 2
  5 =  —  =  —————
    1    2 Â
STEP
7
:
Pulling out like terms :
7.1 Â Â Pull out like factors :
 -17x2 - 14x  =  -x • (17x + 14)
Adding fractions that have a common denominator :
7.2 Â Â Â Adding up the two equivalent fractions
-x • (17x+14) + 5 • 2   -17x2 - 14x + 10
—————————————————————  =  ————————————————
     2            2    Â
STEP
8
:
Pulling out like terms :
8.1 Â Â Pull out like factors :
 -17x2 - 14x + 10  =  -1 • (17x2 + 14x - 10)
Trying to factor by splitting the middle term
8.2   Factoring  17x2 + 14x - 10
The first term is,  17x2  its coefficient is  17 .
The middle term is,  +14x  its coefficient is  14 .
The last term, "the constant", is  -10
Step-1 : Multiply the coefficient of the first term by the constant  17 • -10 = -170
Step-2 : Find two factors of  -170  whose sum equals the coefficient of the middle term, which is  14 .
   -170   +   1   =   -169
   -85   +   2   =   -83
   -34   +   5   =   -29
   -17   +   10   =   -7
   -10   +   17   =   7
   -5   +   34   =   29
   -2   +   85   =   83
   -1   +   170   =   169
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
 -17x2 - 14x + 10
 ————————————————
    2    Â