Solve `2x^2-4x-3=0` by completing the square.
(1) In order to complete the square, the leading coefficient should be 1 so divide both sides by 2:
(2) Now we add a number so that the first three terms form a perfect square trinomial. We take 1/2 of the coefficient of the klinear term and square it.
`x^2-2x+1-1-3/2=0` . To preserve the equality we added a 1 and a -1, effectively adding zero to the left side.
(3) The first three terms form a perfect square trinomial and can be rewritten. We also combine the constant terms:
`x-1=+-sqrt(5/2)` Rationalizing to get rid of the radical in the denominator and adding 1 yields:
`x=1+-(sqrt(10))/2` which is the result.