Choose a method: x(x + 4) = 12 Step by Step

Step by step

The question

Question: choose a method and solve x² + 4x = 12.

x² + 4x = 12

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? ✗

x² has no number in front, and two whole numbers work.

So it factors.

So: factoring.

2. factors easily? ✓ factoring

2 Get 0 on one side

To solve it, we want 0 on the right side.

So we take away 12 on both sides.

We do it on both sides, so they stay equal.

x² + 4x − 12 = 12 − 12

Now we have x² + 4x − 12 = 0.

x² + 4x − 12 = 0

3 Factor

We need two numbers.

They multiply to −12, and they add to 4.

? × ? = −12

? + ? = 4

They multiply to a minus number, so one number is plus and one is minus.

They add to a plus number, so the bigger one is plus.

× is − → one +, one −; bigger one +

We list the pairs that make 12, smallest first.

We take the smaller from the bigger.

We need 4.

2 and 6 give 4.

Yes!

With the signs: −2 and 6.

1 × 12: 12 − 1 = 11

2 × 6: 6 − 2 = 4 ✓

So it is (x − 2)(x + 6) = 0.

(x − 2)(x + 6) = 0

4 One bracket is 0

Two numbers multiply to 0.

That only happens if one of them is 0.

So one bracket must be 0.

A × B = 0 → A = 0 or B = 0

We make each bracket 0.

Two small equations.

x − 2 = 0 or x + 6 = 0

In x − 2 = 0, we add 2 on both sides.

In x + 6 = 0, we take away 6 on both sides.

x − 2 + 2 = 0 + 2 or x + 6 − 6 = 0 − 6

So x = 2 or x = −6.

x = 2 or x = −6

5 Check

Let's check: put x = 2 into the left side.

x = 2: 2² + 4(2) = 4 + 8 = 12

We get 12, the same as the right side.

It works!

Now put x = −6 into the left side.

x = −6: (−6)² + 4(−6) = 36 − 24 = 12

We get 12 again, the same as the right side.

So both answers are right!

Let's look back.

First: choose the method.

Then: get 0 on one side.

Then: factor.

Then: one bracket is 0.

Last: check.

Answer