SOLUTION: Please help me, I can not get this to factor- 7x^2+34x-5

Question 93699: Please help me, I can not get this to factor- 7x^2+34x-5
Found 4 solutions by stanbon, praseenakos@yahoo.com, ankor@dixie-net.com, jayanthihemkos@yahoo.com:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
factor- 7x^2+34x-5
= (7x-1)(x+5)
==============
Cheers,
Stan H.
Answer by praseenakos@yahoo.com(507)   (Show Source): You can put this solution on YOUR website!
Question:

Please help me, I can not get this to factor- 7x^2+34x-5

Answer:

Here you can use the method of splitting middle term..

For that you have to find out two numbers so that their sum is +34(that is coefficient of x ) and whose product is -35( that is 7 * -5)

Such two numbers are +35 and -1

Now split the middle term using these two numbers.

==>

Now group the terms as follows...

==>

Now take out the common terms form each group....

==>

Now (1x + 5) is common in both groups, so take it outside.

===> (1x + 5 ) ( 7x + 5 ) = 0,

So the factors of the given equation is

========================================================================

If you want to solve this equation.....

(1x + 5 ) ( 7x + 5 ) = 0

==> either (1x + 5 ) = 0 or ( 7x + 5 ) = 0

(1x + 5 )= 0 ==> and

( 7x + 5 ) = 0 ==> 7x = -5 ==>

Hope you found the explanation useful.

Regards.

Praseena

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
factor-
7x^2 + 34x - 5
:
You can see that 7 only has 1 & 7 as factors
Also 5 has only 5 and 1 as factors
:
You know it will be this because the middle term is 34 (7*5):
(7x__ 1)(x___5)
:
Now just find the signs that will make this thing work
(7x - 1)(x + 5)
:
Check it by FOILing these factors; 7x^2 + 35x - 1x - 5 = 7x^2 + 34x -5
:
Did this help?
Answer by jayanthihemkos@yahoo.com(87)   (Show Source): You can put this solution on YOUR website!
7x^2+34x-5
Here we apply quadratic formula
x= -b+or- sqrt of b^2 -4ac/2a
here a = 7 , b= 34 , c= -5
==> -34 +/- sqrt of (34)^2-( 4*7*-5)/2*7
==> -34 +/- sqrt of 1156+140/14
==> -34+/- sqrt of 1296/14
==> -34 +/- 36/14
==> 2( -17 +/- 18)/2*7 ( 2 is taken as common factor)
==>-17 +/- 18 /7 ( 2 in the numerator and denominator gets cancelled)
x = -17 + 18/ 7 and -17 -18/7
x = 1/7 and x = -35/7 = -5
Hence the solution for x= 1/7 and -5

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