Just a little algebra problem : Radical Equations?

Question

Just doing algebra and i need a little help. note that [2] means that the number before it is squared

I'm solving radical equations, and I have this:

Square root of (110-n) = n

My first guess would be to square both sides, getting 110-n=n[2].

Then .. you'd add n to n[2] ? what would that be ?



thanks everyone [:

Answer 1

Hint: Now you can factor it, or use the quadratic equation.

Answer 2

You're right in squaring both sides of your equation in order to get rid of the square root. That would leave you with 110 - n = n^2. Next just move the numbers from the left side of your equation over to the right side of the equation in order to get your equation looking like this :
n^2 + n - 110. Now you can use the quadratic equation to solve for the values of n that you need. The formula for the quadratic equation is -b plus or minus the square root of b^2 all divided by 2a. Keep in mind that n^2 is considered your a term, n is considered your b term and -110 is considered your c term. Simply fill in the numbers according to the equation. Your equation should be - 1 plus or minus the square root of 1^2 - 4(1)(-110) all divided by 2(1). You should get -1 plus or minus the square root of 141 which ends up being a perfect square root (because you can multiply 21 times 21 to get 410) and comes out of the square root as 21 all divided by 2. Now solve for both of your answers.

n = ( -1 + 21)/ 2 = 10
n = (-1 - 21)/2 = -11

Answer 3

You are right in squaring both sides.....
So then you have:
110-n=n[2]
So now you have a quadratic equation and you have to set the equation equal to 0. Like so:
n[2] + n -110 = 0
Then you have to factor the equation:
(n+11)(n-10)
Then you set both equations equal to 0. Like so:
n+11 = 0 and n-10 = 0
So, 'n' can either equal -11 or 10. There will always be two answers when you have a quadratic.
I hope this helps!

Answer 4

well, if ur a high schooler, i would suggest you adding n to both sides, subtract the 110 and do the quadratic equation. if your a middle schooler,guess and check would work alot better. you usually deal with perfect squares at the beginning, so whats the closest perfect square? its 100. so 110- 10 equals 100 and the square root of that is 10. so we found n.

Answer 5

Try This Link:


http://www.embedded.com/98/9802fe2.htm

Answer 6

Hint: Now you can factor it, or use the quadratic equation.