Why Does My Solution to the Radical Equation Differ from the Answer Key?

[Schaus]

Homework Statement

(Square root)-12 -3x - 3 = 0
Everything underline is supposed to be under the square root sign.

Homework Equations

The Attempt at a Solution

(Square root3x +12)² = (3)²
3x + 12 = 9
-12 -12
3x = -3
x = -1
Solution in this learning guide says the answer is -7. So I'm just wondering where I went wrong.
If anyone knows how to make a square root symbol, please let me know.

 

[Mark44]

Homework Statement

(Square root)-12 -3x - 3 = 0
Everything underline is supposed to be under the square root sign.

Homework Equations

The Attempt at a Solution

(Square root3x +12)² = (3)²

No. Your equation is $\sqrt{-12 - 3x} = 3$
If you square the left side, you get -12 - 3x, not 12 + 3x.

3x + 12 = 9
-12 -12
3x = -3
x = -1
Solution in this learning guide says the answer is -7. So I'm just wondering where I went wrong.
If anyone knows how to make a square root symbol, please let me know.

I get x = -7 as well.

 

[Mark44]

BTW, I changed your thread title from "Solving Ration Equations" to "Solving Radical Equations."
Yours is not a rational equation, which would involve a quotient of two polynomials.

 

[Logical Dog]

 

[Schaus]

I thought you couldn't square a negative number?

 

[Logical Dog]

there is no square root of a negative number, no even nth root of any negative number

I thought you couldn't square a negative number?

there are odd nth roots of negative numbers...

eg square root of -1 is not a real number, but cube root of -1 is -1.

 

[Schaus]

So as long as there are undefined units then you can square it?

 

[Logical Dog]

Sorry If I am confusing, all variables like X Y evaluate to a number, the squaring of a negative number is positive.

The square root or even nth root of a negative number is not defined in terms of a real number.

You can square a negative number to get a positive.

-1 *-1 = 1.

sQAURE ROOT =/= squaring.

 

[Schaus]

Ohhh, duh. Sorry! I understand now.

 

[Ray Vickson]

I thought you couldn't square a negative number?

Of course you can square a negative number. That is why an equation like $x^2 = 9$ has two solutions: $x = 3$ and $x = -3$. Both give 9 when you square them.

Perhaps you meant that you cannot take the square root of a negative number (in the real number system). But in the complex number field we can very nicely take the square root of a negative number, to get a so-called imaginary number. (It might surprise you to know that such things are used all the time by physicists and electrical engineers, among others.)