Question 75531
The solutions of 3/4(x+1)^2=9


The given equation is {{{3(x + 1)^2/4}}} = 9 


This can be written as {{{3(x + 1)^2 = 36}}} 


Simplifying this further, we get: 


{{{3(x^2 + 1 + 2x)= 36}}} 


{{{3x^2 + 3 + 6x - 36 = 0}}} 


{{{3x^2 + 6x - 33 = 0}}}


This can be solved by using the quadratic formula. 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


Hence, the roots of the equation are:  


{{{x = (-6 +- sqrt( 6^2-4*(3)*(-33) ))/(2*3) }}} 


{{{x = (-6 +- sqrt(36 - (-396)))/(6) }}}


{{{x = (-6 +- sqrt(432))/6}}}


{{{x = (-6 +- sqrt(36 X 12))/6}}} 


{{{x = (-6 +- 6 sqrt(12))/6}}} 


{{{x = -1 +- sqrt(12)}}} 


hence, the solution