Choose a method: 2x^2 - 8x = 0 Step by Step

Step by step

The question

Question: choose a method and solve 2x² − 8x = 0.

2x² − 8x = 0

1 Choose the method

We ask in order.

First: is there no x term?

No, there is one.

1. no x term, or ( )² = k? ✗

There is no plain number.

Both parts have x in them, so we can take x out.

So: factoring.

2. factors easily? ✓ factoring

2 Divide by 2

Easy way first: every number can be divided by 2.

So we divide both sides by 2.

0 divided by 2 is still 0.

2, -8, 0: all divide by 2

Now we have x² − 4x = 0.

x² − 4x = 0

3 Factor

There is no plain number.

Both parts have x in them.

So we take x out.

x² = x × x, −4x = x × (−4)

So it is x(x − 4) = 0.

x(x − 4) = 0

Careful!

Don't divide both sides by x.

Then the answer x = 0 would be lost.

Careful: don't divide by x. We would lose x = 0.

4 One bracket is 0

x times the bracket is 0.

That only happens if one of them is 0.

A × B = 0 → A = 0 or B = 0

We make each part 0.

Two small equations.

x = 0 or x − 4 = 0

x = 0 is done already.

In x − 4 = 0, we add 4 on both sides.

x = 0 or x − 4 + 4 = 0 + 4

So x = 0 or x = 4.

x = 0 or x = 4

5 Check

Let's check: put x = 0 into the left side.

x = 0: 2(0)² − 8(0) = 0 + 0 = 0

We get 0, the same as the right side.

It works!

Now put x = 4 into the left side.

x = 4: 2(4)² − 8(4) = 32 − 32 = 0

We get 0 again, the same as the right side.

So both answers are right!

Let's look back.

First: choose the method.

Then: divide by 2.

Then: factor.

Then: one bracket is 0.

Last: check.

Answer