# Why is x^2 = -1 not a possible solution for x in the equation x^2 + 1 = 0?

In summary: If x was supposed to be real then, the equation has no solution, but since we are considering complex numbers the equation has a solution!

X^2 + 1 = 0

## Homework Equations

find the solution

## The Attempt at a Solution

As simple as this:

what is the solution to x^2 +1 = 0

... my question, why am I wrong in thinking x^2 = -1 as a possible solution?

X^2 = -1 is not a solution for "what is x", which is what is being asked for, it is a solution to "what is X^2"

phinds said:
X^2 = -1 is not a solution for "what is x", which is what is being asked for, it is a solution to "what is X^2"

Oh I see... Well, a solution to x^2 could be $$\pm 1$$. So what is the solution, I am a bit confused. Would it be

x = -1/2

Oh I see... Well, a solution to x^2 could be $$\pm 1$$. So what is the solution, I am a bit confused. Would it be

x = -1/2

(-1/2)² = 1/4, so that's not a solution to X² + 1 =0

You are right in re-arranging your equation as X² = -1
now take the square root of both sides.

Some information is missing here. What is x supposed to be?? Is it rational? Real? Complex?
Whether or not a solution exists to this problem depends on what you allow x to be.

Oh I see... Well, a solution to x^2 could be $$\pm 1$$.
No, it's not. You have already said that x^2= -1, not $\pm 1$. Now you need to get x itself, not x^2. You need to "undo" the square- what's the opposite of squaring?

So what is the solution, I am a bit confused. Would it be

x = -1/2
You seem to be confused about what "solution to an equation" means. What level mathematics are you taking? Where did you get this problem? Have you studied complex numbers.

NascentOxygen said:
(-1/2)² = 1/4, so that's not a solution to X² + 1 =0

You are right in re-arranging your equation as X² = -1
now take the square root of both sides.

So the solution is

$$x = \sqrt{-1}$$

So the solution is

$$x = \sqrt{-1}$$

Bravo.

So the solution is

$$x = \sqrt{-1}$$

$$x=\pm\sqrt{-1}$$

Mentallic said:
$$x=\pm\sqrt{-1}$$
To the OP: you know the symbol we use for $\sqrt{-1}$, right?

Yes, it's the imaginary number. :)

Yes, it's the imaginary number. :)

Which imaginary number?

ehild

Yes, it's the imaginary number. :)

ehild said:
Which imaginary number?
In other words, what symbol do we use to represent ##\sqrt{-1}##?

i = sqrt{-1}

i = sqrt{-1}
Right

That's right! If x was supposed to be real then, the equation has no solution, but since we are considering complex numbers the equation has a solution!

For the fundamental theorem of Algebra a polynomial form has always a solution in the set of the complex numebers.

## What is a simple equation?

A simple equation is a mathematical expression that contains one or more variables and an equal sign, which shows that the value on the left side is equal to the value on the right side.

## What is a solution to a simple equation?

A solution to a simple equation is a value or set of values that make the equation true when substituted for the variables. It is also known as the answer to the equation.

## How do you solve a simple equation?

To solve a simple equation, you must isolate the variable on one side of the equal sign and move all other constants and variables to the other side. This can be done by using inverse operations, such as addition, subtraction, multiplication, and division.

## What is the importance of finding a solution to a simple equation?

Finding a solution to a simple equation is important because it helps us understand the relationship between different quantities and allows us to make predictions and solve real-life problems. It also serves as a basis for more complex math concepts.

## What are some common mistakes when solving a simple equation?

Some common mistakes when solving a simple equation include forgetting to perform the same operation on both sides, making a calculation error, or forgetting to check the solution in the original equation. It is important to double-check your work and use a systematic approach to avoid these mistakes.

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