Question

Complete the square to solve for x:

2x∧2-5x-3=0

Answer 1

`2x^2-5x-3=0\ \ \ \ \ |divide\ both\ isdes\ by\ 2\\\\x^2-2.5x-1.5=0\\\\x^2-2x*1.25=1.5\\\\x^2-2x*1.25+1.25^2-1.25^2=1.5\\\\\underbrace{x^2-2x*1.25+1.25^2}_(use:(a-b)^2=a^2-2ab+b^2)=1.5+1,5625\\\\(x-1.25)^2=3.0625\iff x-1.25=√(3.0625)\ or\ x-1.25=-√(3.0625)\\\\x-1.25=1.75\ or\ x-1.25=-1.75\\\\x=1.75+1.25\ or\ x=-1.75+1.25\\\\\boxed{x=3\ or\ x=-0.5}`