Simplify x^2 + 9 = 0 using i

Step by step

The question

Question: solve x² + 9 = 0 using i.

No real number times itself is negative.

So we use a new number: i, the square root of minus 1.

So i squared is minus 1.

1 Get x² alone

The + 9 is in the way.

To remove + 9, we take away 9.

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

+ 9 and − 9 make zero.

Cross them out.

0 minus 9 is −9.

Before i, we could not solve this.

Now it has two answers.

2 Square root of both sides

Something squared is minus 9.

So that something is the square root of minus 9, or minus it.

Both work, because minus times minus is plus.

So x is the square root of minus 9, or minus it.

√(−9) is √9 times √(−1): 3 times i.

So x = 3i or x = −3i.

3 Check

Let's check 3i.

(3i)² is 9 times i², that is −9.

We get 0.

Now −3i.

We get 0 again.

Both answers work!

Let's look back.

First: get x² alone.

Then: square root of both sides.

Last: check.