Write as #2(x^2+3/2x)-5+k=0.......Equation(1)#
Where #k# is a constant of correction that compensates for the error introduce whilst manipulating the equation.
Take the power outside the bracket.
#2(x+3/2x)^2-5+k=0#
Remove the #x# from #3/2x#
#2(x+3/2)^2-5+k=0#
Halve the #3/2#
#2(x+3/4)^2-5+k=0#
#color(red)("The error comes from")#
#color(red)(2)(x+color(red)(3/4))^(color(red)(2))-5+k=0...Equation(1_a)#
.................................................................................................................
in that we have #color(red)(2xx(3/4)^2)+k=0 larr" building the error correction"#
#=>k=-(2xx9/16) = -18/16 = -9/8#
.....................................................................................................................
#=>2(x+3/4)^2-5-9/8=0#
#=>color(blue)(2(x+3/4)^2-49/8=0)....................Equation(1_b)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#(x+3/4)^2=49/16#
#x+3/4=+-sqrt(49/16)" "=" "+-7/4#
#x=+-7/4-3/4#
#x=-10/4 " and "1#
#color(red)(x=-5/2 " and "1)#
