Question 93699
Question:


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


Answer:

 

{{{ 7x^2 + 34x -5 = 0 }}} 



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.


==> {{{ 7x^2 + 35x - 1x  -5 = 0 }}} 


Now group the terms as follows...



==> {{{ (7x^2 + 35x) - (1x + 5)  = 0 }}} 


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



==> {{{ 7x( 1x  +  5 ) - 1(1x + 5)  = 0 }}} 


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 {{{( x + 5 ) and ( 7x + 5 ) }}} 


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


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


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




(1x + 5 )= 0 ==> {{{x = -5 }}}and 


 ( 7x + 5 ) = 0 ==> 7x = -5 ==> {{{ x = -5/7}}}




Hope you found the explanation useful.



Regards.



Praseena