Lesson video

Hi, I'm Miss Davis.

In this lesson, we're going to be solving quadratic equations by completing the square.

In this first example, we've been asked to solve the equation without expanding the bracket.

The first thing that we're going to do is to add 16 to both sides of the equation, giving us X subtract three squared is equal to 16.

Next, we're going to square root both sides of the equation.

This gives us X subtract three is equal to positive or negative four, we can then add three to both sides to give X is equal to three, add or subtract four.

This gives solutions of X is equal to seven or X is equal to negative one.

Here are some questions for you to try.

Pause the video to complete your task and review once you're finished.

Here are the answers.

All of the B values that are added or subtracted to the square bracket or square numbers.

This means that we get an integer solution.

In this next example, we are going to solve the equation without expanding the bracket giving our solution in exact form.

We're going to start off by adding 10 to both sides, giving X subtract three, all squared, is equal to 10.

Then we'll square root both sides, giving X subtract three is equal to positive or negative the square root of 10.

As 10 is not a square number, this is the exact form of the square root of 10.

We can then add three to both sides.

This gives us the two solutions of X is equal to three, add the square root of 10 or X is equal to three subtract the square root of 10.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The question specifies to leave the answers in exact form.

This means that all the solutions should have a square root in them.

In this next example, we haven't been given, the completed square for writing X squared, add 10X, add 20, in completed square form is going to be our first step.

This gives us X add five or squared subtract five, this is still equal to zero.

Now, we can begin to solve the equation.

Our first step with this is to add five to both sides.

This gives that X add five squared is equal to five.

We can then square root both sides, giving X add five is equal to positive or negative the square root of five.

We can then subtract five from both sides.

This gives the two solutions of X is equal to negative five, add the square root of five or X is equal to negative five subtract the square root of five.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

You could convert these answers into decimal form, but the question specifies for it to be left in exact form, so we're just going to leave these as they are.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

The square roots in these solutions could be simplified.

If you haven't looked at Surds yet, this will help you with this type of question.

That's all for this lesson.

Thanks for watching.