# data[].attributes.attachment_link.title
Solve quadratic equations: complex solutions

# data[].attributes.attachment_link.description
Solve quadratic equations using the quadratic formula. Some of the equations have real solutions while others have complex solutions.

# data[].attributes.attachment_link.readable_text
Some quadratic equations cannot be solved by factorising and so an alternative method is the quadratic formula. It is based on a method called completing the square.

Rule to remember:

[latex]\text{Then it can be shown that} \hphantom{aaa} x=\dfrac{- b \pm \sqrt {{b^2} - 4ac}}{2a}[/latex]

This tutorial shows you when to use it, clues that are given in a question and common mistakes that are often made.

How to Derive the Quadratic Formula

# data[].attributes.attachment_link.description
Some quadratic equations cannot be solved by factorising and so an alternative method is the quadratic formula. It is based on a method called completing the square.

# data[].attributes.attachment_link.description
In this tutorial you are shown how to solve a quadratic equation by using the method of completing the square. This is often used when a quadratic equation does not factorise.

# data[].attributes.attachment_link.description
All quadratic equations have the form a{x^2} + bx + c = 0\hphantom{aaa} \text{where}\hphantom{aaa}a \ne 0 If a quadratic equation factorises then we can solve it by using a factorising method as shown in this video.

# data[].attributes.attachment_link.title
Exam Questions - Solved by the quadratic formula

# data[].attributes.attachment_link.description
Solving 6x²+3=2x-6 by rewriting in standard form and identifying the parameters a, b, and c, that can be used within the quadratic formula.

# data[].attributes.headline
Number of solutions of quadratic equations (practice) 

# data[].attributes.subject
Number of solutions of quadratic equations (practice) 

# data[].attributes.attachment_link.title
Number of solutions of quadratic equations

# data[].attributes.attachment_link.description
Analyze quadratic equations in order to determine how many different real number solutions they have.

# data[].attributes.headline
Practice your quadratic equation skills 

# data[].attributes.subject
Practice your quadratic equation skills 

# data[].attributes.attachment_link.readable_text
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# data[].attributes.attachment_link.title
Solve quadratic equations with the quadratic formula (practice) | Khan Academy

# data[].attributes.attachment_link.description
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.