Choose a method: x^2 - 7x = 0 Step by Step

Step by step

The question

Question: choose a method and solve x² − 7x = 0.

x² − 7x = 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 Factor

There is no plain number.

Both parts have x in them.

So we take x out.

x² = x × x, −7x = x × (−7)

So it is x(x − 7) = 0.

x(x − 7) = 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.

3 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 − 7 = 0

x = 0 is done already.

In x − 7 = 0, we add 7 on both sides.

x = 0 or x − 7 + 7 = 0 + 7

So x = 0 or x = 7.

x = 0 or x = 7

4 Check

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

x = 0: 0² − 7(0) = 0 + 0 = 0

We get 0, the same as the right side.

It works!

Now put x = 7 into the left side.

x = 7: 7² − 7(7) = 49 − 49 = 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: factor.

Then: one bracket is 0.

Last: check.

Answer