SOLUTION: please help with the equation {{{4-4y-y^2=0}}} I know you have to rewrite it to get the proper form...but then the negative is in the front, so what would I do next?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: please help with the equation {{{4-4y-y^2=0}}} I know you have to rewrite it to get the proper form...but then the negative is in the front, so what would I do next?      Log On


   

Question 40549: please help
with the equation 4-4y-y%5E2=0 I know you have to rewrite it to get the proper form...but then the negative is in the front, so what would I do next?
Found 2 solutions by stanbon, abcdefg:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
4-4y-y^2=0
Multiply through be -1 or get the same result by transposing
the left to the right side of the equal sign. In either case
you get:
y^2+4y-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B4y%2B-4+=+0) has the following solutons:

y%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=%284%29%5E2-4%2A1%2A-4=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+32+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%284%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+0.82842712474619
y%5B2%5D+=+%28-%284%29-sqrt%28+32+%29%29%2F2%5C1+=+-4.82842712474619

Quadratic expression 1y%5E2%2B4y%2B-4 can be factored:
1y%5E2%2B4y%2B-4+=+1%28y-0.82842712474619%29%2A%28y--4.82842712474619%29
Again, the answer is: 0.82842712474619, -4.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-4+%29

Hope this helps.
Cheers,
Stan H.

Answer by abcdefg(37) About Me  (Show Source):
You can put this solution on YOUR website!
4-4y-y^2=0
change to
-y-4y-4=0
(-y+2)(y-2)=0
-----------
solve for y
(-y+2)=0
(-y+2-2)=0-2
(-y)=-2
divide by -1
y=2
-----------
(y-2)=0
(y-2+2)=0+2
y=2
so the answer is y=2