# Simplifying Equation With Square Root

1. Jan 26, 2008

### kwikness

1. The problem statement, all variables and given/known data
An equation in a book lists this equation:
(c - 18)$$^{2}$$ = (-3$$\sqrt{c})$$$$^{2}$$

And it simplifies it as:
c$$^{2}$$ -45c + 324 = 0

2. The attempt at a solution
When I do out the equation, I get:
c$$^{2}$$ + 324 = 9 + c

i squared c, then -18 for the left side of the equation, then for the right side, I squared -3 to get 9, then $$\sqrt{c}$$, which is c.

Last edited: Jan 26, 2008
2. Jan 26, 2008

### Hootenanny

Staff Emeritus
Hi kwikness and welcome to PF,

Firstly, note that;

$$\left(a+b\right)^2 \neq a^2+b^2$$

Rather,

$$\left(a+b\right)^2 = \left(a+b\right)\cdot\left(a+b\right) = a^2 +2ab + b^2$$

Secondly,

$$(-3)^2 \neq 324$$

And thirdly;

$$(a\cdot b)^2 \neq a^2+b^2$$

Rather,

$$(a\cdot b)^2 = a^2\cdot b^2$$

Last edited: Jan 26, 2008
3. Jan 26, 2008

### kwikness

Sorry, I meant 9 =)

I made my mistake when I forgot to "FOIL" the left-hand side of the equation. When I do so, I get:

C$$^{2}$$ -45c + 324 = 0

Thank you very much for clearing that up for me. I'm in a bit of a situation. I'm a good student in my 4th semester of college. In high school, I was able to slide by my math classes. I half-assed Algebra I, did okay in Geometry, and took no other math courses. Now I find myself in Calculus I, 5 years after my last math class. The first thing my professor said was, "You're not going to pass this course unless you've had Trigonometry and Pre-Calculus.", which I haven't. I'm now trying to backtrack and learn these courses myself with the aid of video tutorials and practicing problems on my own time. I excel in every subject at school but math. It's such a weakness for me and I'm now just starting to do something about it.

Any pointers are appreciated, thanks again for your help.

4. Jan 27, 2008

### Staff: Mentor

One needs to know the solution to the quadratic equation.

Alternatively, one recognizes (c+a)(c+b) = c2 + (a+b)c + ab = c2 - 45c + 324, so what does one do with corresponding coefficients?