Question

2a^2-a-3=0 solve by completing the square

Answer 1

Pattern:

`\mathrm{Let's\ take\ a\ quadratic\ equation:}\\px^2+qx+r=0\\\mathrm{or,\ }px^2+qx=-r\\\mathrm{Multiplying}\ '4p'\mathrm{\ on \ both\ sides,}\\\mathrm{or,\ }4p^2x^2+4pqx=-4pr\\\mathrm{Adding\ }q^2\ \mathrm{on\ both\ sides,}\\\mathrm{or,\ }4p^2x^2+4pqx+q^2=q^2-4pr\\\mathrm{or,\ }(2px+q)^2=q^2-4pr\\\mathrm{or,\ }2px+q=\pm√(q^2-4pr)\\\mathrm{or,\ }x=(-q\pm√(q^2-4pr))/(2p)`

Answer:

`2a^2-a-3=0\\\mathrm{or,\ }2a^2-a=3\\\mathrm{or,\ }8(2a^2-a)=8(3)\ \ \ \ \mathrm{[Multiply\ '4p'='4(2)' on \ both\ sides]}\\\mathrm{or,\ }16a^2-8a=24\\\mathrm{or,\ }16a^2-8a+(-1)^2=24+(-1)^2\mathrm{[Add\ 'q^2=(-1)^2'\ on\ both\ sides.]}\\\mathrm{or,\ }16a^2-8a+1=25\\\mathrm{or,\ }(4a-1)^2=25\\\mathrm{or,\ }4a-1=\pm 5\\\mathrm{or,\ }4a=1\pm5\\\mathrm{i.e.\ }a=(3)/(2),-1`