Choose a method: 2x^2 + 4x - 6 = 0 Step by Step

Step by step

The question

Question: choose a method and solve 2x² + 4x − 6 = 0.

2x² + 4x − 6 = 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? ✗

After dividing by 2, x² has no number in front, and two whole numbers work.

So it factors.

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, 4, -6: all divide by 2

Now we have x² + 2x − 3 = 0.

x² + 2x − 3 = 0

3 Factor

We need two numbers.

They multiply to −3, and they add to 2.

? × ? = −3

? + ? = 2

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 3, smallest first.

We take the smaller from the bigger.

We need 2.

1 and 3 give 2.

Yes!

With the signs: −1 and 3.

1 × 3: 3 − 1 = 2 ✓

So it is (x − 1)(x + 3) = 0.

(x − 1)(x + 3) = 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 − 1 = 0 or x + 3 = 0

In x − 1 = 0, we add 1 on both sides.

In x + 3 = 0, we take away 3 on both sides.

x − 1 + 1 = 0 + 1 or x + 3 − 3 = 0 − 3

So x = 1 or x = −3.

x = 1 or x = −3

5 Check

Let's check: put x = 1 into the left side.

x = 1: 2(1)² + 4(1) − 6 = 2 + 4 − 6 = 0

We get 0, the same as the right side.

It works!

Now put x = −3 into the left side.

x = −3: 2(−3)² + 4(−3) − 6 = 18 − 12 − 6

= 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