Question 93704
Question:


Please help me find the value of x in this equation.
x^2+2x=8


Answer :

{{{ x^2 + 2x = 8 }}}


Subtract 8 from both sides( then it will be in the standard form of a quadratic equation)



==> {{{ x^2 + 2x  - 8 = 8 - 8  }}}


==> {{{ x^2 + 2x - 8 = 0 }}}



You can solve it by using quadratic formula as well as splitting the middle term.



Method of splitting middle term:


{{{ x^2 + 2x - 8 = 0 }}}


Here you need to find out two numbers whose sum is +2 (coefficient of x) and whose product is -8( that is the constant term)



Such two numbers are +4 and -2


==> {{{ x^2 + 4x- 2x - 8 = 0 }}}


Now group the terms.


==> {{{ (x^2 + 4x) - (2x + 8 )= 0 }}}



Now take out the common terms from each group.



==> {{{ x(x  + 4 ) - 2( x + 4)= 0 }}}



Here (x + 4 ) is common in both the groups, so you can take it outside...



==> (x + 4 ) ( x - 2) = 0



==> either (x + 4 ) = 0 or  ( x - 2) = 0



==> (x + 4 ) = 0 ==> x = -4 and 


 ( x - 2) = 0  ==> x = 2



So the value of  x is  either {{{-4}}} or {{{2}}}



Hope you found the explanation useful.



Regards.


Praseena.