Simplifying Equation With Square Root

kwikness

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

And it simplifies it as:
c[tex]^{2}[/tex] -45c + 324 = 0


2. The attempt at a solution
When I do out the equation, I get:
c[tex]^{2}[/tex] + 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 [tex]\sqrt{c}[/tex], which is c.

Hootenanny

Hi kwikness and welcome to PF,

Firstly, note that;

[tex]\left(a+b\right)^2 \neq a^2+b^2[/tex]

Rather,

[tex]\left(a+b\right)^2 = \left(a+b\right)\cdot\left(a+b\right) = a^2 +2ab + b^2[/tex]

Secondly,

[tex](-3)^2 \neq 324[/tex]

And thirdly;

[tex](a\cdot b)^2 \neq a^2+b^2[/tex]

Rather,

[tex](a\cdot b)^2 = a^2\cdot b^2[/tex]

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[tex]^{2}[/tex] -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?