How did this equation end up with the value x006 what was th

Solution

first of all we have to perform cross multiply ,then we get

4x²=0.25 (0.5-2x)² (0.5-x)

performing square of 0.5-x ,we get

4x²=0.25(0.25+4x²-2x) (0.5-x)

multiplying the equation variables on right hand side to simplify it ,we get

4x²=0.25(0.125+2x²-x-0.25x-4x³+2x²)

or 4/0.25 x²=-4x³+4x²-1.25x+0.125

taking terms from rhs to lhs to keep x³ constant positive

4x³+12x²+1.25x-0.125=0

now this equation is not factorised properly,so we have to take trial & error method to find the solution

If we use any negative value to x we find that result will be a negative no.,hence solution will be a positive number inetger or fraction,now if we put x=1 in the equation we get 17.125 which is a positive no.,this indicates that the solution will be in between the open interval (0,,1),now but putting x=0.5,0.2,0.1,0.05 at last we find that 0.06 is the solution of the equation.