Solve real-coefficient quadratic equations that have complex solutions.
Rewrite quadratic-formula solutions with a negative square root in standard complex form
Problem
Simplify \(x=(4\pm~\sqrt{-36})/2\) by rewriting \(\sqrt{-36}=6i\) and dividing \(\text{both}~\text{the}~\text{real}~\text{and}~\text{imaginary}~\text{terms}\) by \(2\).
Big Picture
What this problem is really about
Standardizing quadratic-formula output requires simplifying the negative radical and distributing the denominator across the entire numerator. We’ll convert the radical to an imaginary term, preserve the plus-minus pair, divide both components, and state the conjugates in a plus b i form.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
