You can put this solution on YOUR website!
Complete the square on
Step 1, starting from a quadratic in standard form like you have is to put the constant term on the right:
Step 2, if the coefficient on the
term is other than 1, divide by that coefficient.
Step 3, divide the resulting coefficient on the
term by 2 and square the result
Step 4, add this result to both sides of your equation and collect terms
Step 5, the above result has a perfect square on the left (hence the term "completing the square"), so factor it:
Step 6, take the square root of both sides:
Which leads us to a great big oops! because you can't take the square root of a negative number. The solution is to use the imaginary number
which is defined as
, leaving us with:
Step 7, isolate
and simplify in each equation
If you want the exact representation of the roots of the given equation, you are done. If you need a numerical approximation of the imaginary parts of your complex numbers, get out your calculator.
to verify that the product is, in fact,
, is left as an exercise for the student. Alternatively, you could just trust me.