SOLUTION: Hi, i've literally tried everything to find out about the quadratic formula; can you help me solve this? {{{4k^2-81=0}}} directions say "solve equation with the quadratic formula

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, i've literally tried everything to find out about the quadratic formula; can you help me solve this? {{{4k^2-81=0}}} directions say "solve equation with the quadratic formula      Log On


   

Question 474168: Hi, i've literally tried everything to find out about the quadratic formula; can you help me solve this?
4k%5E2-81=0
directions say "solve equation with the quadratic formula"
thanks! (:
Found 3 solutions by Alan3354, ewatrrr, richard1234:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B0x%2B-81+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A4%2A-81=1296.

Discriminant d=1296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+1296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+1296+%29%29%2F2%5C4+=+4.5
x%5B2%5D+=+%28-%280%29-sqrt%28+1296+%29%29%2F2%5C4+=+-4.5

Quadratic expression 4x%5E2%2B0x%2B-81 can be factored:
4x%5E2%2B0x%2B-81+=+%28x-4.5%29%2A%28x--4.5%29
Again, the answer is: 4.5, -4.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B0%2Ax%2B-81+%29

k = x

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

4k%5E2-81=0

 (2k)^2 - 81 = 0

2k+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

2k+=+%28-0+%2B-+sqrt%28+324%29%29%2F%282%29+

    2k = ± 9

     k = ± 4.5



CHECKING our Answers***

 4*(4.5)^2 - 81 = 0

 4*(-4.5)^2 - 81 = 0

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic formula is quite straightforward, it says that the roots of a quadratic in the form ax^2 + bx + c = 0 are



Here, the only tricky spots (and they shouldn't be tricky after a little while!) are that the quadratic is in terms of k, and there is no k term. However this is quite simple, we just write the quadratic as 4k^2 + 0k - 81 = 0, and set a = 4, b = 0, c = -81.