Simplifying Equation With Square Root

[kwikness]

Homework Statement

An equation in a book lists this equation:
(c - 18)^{2} = (-3\sqrt{c})^{2}

And it simplifies it as:
c^{2} -45c + 324 = 02. 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.

 

[Hootenanny]

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

 

[kwikness]

I squared -3 to get 324

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.

 

[Astronuc]

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?