For this problem,
we want to solve for x in the equation
two x squared plus eight
x plus 26 equals zero.
First, we wanna divide both
sides of the equation by two
to get x squared plus four
x plus 13 equals zero.
Since the left side can't factor out,
we're gonna use the quadratic
formula to solve for x.
In this equation a equals one,
b equals four and c equals 13.
So using the quadratic formula,
we get x equals negative four
plus or minus the square
root of four squared
minus four times one times 13,
all over two times one.
This equals negative four plus or minus
the square root of
negative 36 all over two.
Since we have a negative number
underneath the square root,
there are no real solutions for x.
However, we can use i to
solve for a complex solution.
So we can rewrite this as negative four
plus or minus the square
root of negative one
times the square root of 36, all over two.
This equals negative four
plus or minus six i over two.
If we divide the numerator by two,
this becomes negative two
plus or minus three i,
so x equals negative two plus three i,
or negative two minus three i.
This is the final answer.
