Question 89118
{{{2x^2+8x+5=0}}}
First, put the x^2 and x terms alone on one side of the equation:
{{{2x^2+8x=-5}}}
You need to be sure the coefficient of x^2 is 1, so divide all terms by 2:
{{{x^2+4x=-5/2}}}
Divide the coefficient of x by 2 and square the result. Add this to both sides of the equation in order to maintain the equality.
{{{x^2+4x+4=-5/2+4}}}
Simplify right hand side:
{{{x^2+4x+4=3/2}}}
Now, the left hand side can be written as a perfect square:
{{{(x+2)^2=3/2}}}
Take the square root of both sides:
x+2=+-sqrt(3/2)
Solve for x:
{{{highlight(x=-2+-sqrt(3/2))}}}
You can plug this into a calculator if you need a numerical answer, but this is usually good enough.
Good Luck,
tutor_paul@yahoo.com