Solving quadratic equations by completing the square
0/1
Introduction
Lessons
Solve by completing the square: 2x2−12x+10=0
0/3
Examples
Lessons
Solving a quadratic equation with TWO REAL SOLUTIONS
Solve by completing the square: x2+10x+6=0
Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION
Solve by completing the square: 9x2+25=30x
Solving a quadratic equation with TWO COMPLEX SOLUTIONS
Solve by completing the square: −3x2−24x=49
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
Make Use of Our Learning Aids
Last Viewed
Practice Accuracy
Suggested Tasks
Get quick access to the topic you're currently learning.
See how well your practice sessions are going over time.
Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
Create and Customize Your Avatar
Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.
4-step approach:
1. isolate X's on one side of the equation
2. factor out the leading coefficient of X2
3. "completing the square" • X-side: inside the bracket, add (half of the coefficient of X)2 • Y-side: add [ leading coefficient⋅ (half of the coefficient of X)2 ]
4. clean up • X-side: convert to perfect-square form • Y-side: clean up the algebra