Question 89199
Question 

Find the solution sets.

4x^2 - 25 = 0


Answer.



{{{ 4x^2 - 25 = 0 }}}



This can be written as .....


{{{ (2x)^2 - 25 = 0 }}}, which is of the form, {{{ a^2 - b^2}}}



We know that {{{ a^2 - b^2}}} can be written as, 
{{{ a^2 - b^2}}}= (a + b) ( a - b)


Similarly 


{{{ (2x)^2 - 25 = 0 }}} ==> (2x + 5)( 2x - 5 ) = 0


==> either (2x + 5) = 0  or ( 2x - 5 ) = 0



==> 2x + 5 = 0   

Subtract 5 from both sides.....


==> 2x - 5 - 5 = 0 - 5
    

==> 2x = -5  


Divide both sides by 2


==> {{{ 2x/2 = -5/2 }}}



==> {{{ x = -2.5 }}}


Now  suppose  2x-5 = 0 


Add 5 on both sides....



2x - 5 + 5 = 0 + 5





==> 2x = 5



Divide both sides by 2



==> {{{2x/2 = 5/2}}}



==> {{{ x = 2.5}}}



So the solution set is = { 2.5, -2.5 }




Hope you found the explanation useful.



Regards.

Praseena