Question 79089
{{{2x^2 + 8x + 3 = 0}}}
subtract 3 from both sides
{{{2x^2 + 8x = -3}}}
divide both sides by 2
{{{x^2 + 4x = -(3/2)}}}
Now you operate on the left side to complete square
and put the same thing on both sides so the equation is not changed
{{{x^2 + 4x + (4/2)^2 = -(3/2) + (4/2)^2}}}
{{{x^2 + 4x + 4 = 5/2}}}
{{{(x + 2)^2 = 5/2}}}
{{{(x + 2) = 0 +- sqrt(5/2)}}}
{{{x = -2 +- sqrt(5/2)}}} answer
You can check these answers by plugging back into original
equation. It's a good excercise for you