SOLUTION: Solve. (y+5)(y-1)=27

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Question 246150: Solve.
(y+5)(y-1)=27
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(y+5)(y-1)=27
expand
y^2+4y-5=27
add 5 to both sides
y^2+4y=32
we will complete the square
take (4/2)^2 which =4
add 4 to both sides
y^2+4y+4=36
factor
(y+2)^2=36
get square root
y+2=+\-6
y+2=6
y+2=-6
subtract 2 from both sides
y=4
y=-8
see below for other ways to do it
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-32+=+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=%284%29%5E2-4%2A1%2A-32=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%284%29-sqrt%28+144+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B4x%2B-32 can be factored:
1x%5E2%2B4x%2B-32+=+1%28x-4%29%2A%28x--8%29
Again, the answer is: 4, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-32+%29

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Given the setup:
%28y%2B5%29%28y-1%29+=+27
.
We can multiply through:
y%5E2+-y+%2B5y+-+5+=+27
.
Collecting terms
y%5E2+%2B+4y+-+5+=+27
.
Subtracting 27 from both sides
y%5E2+%2B+4y+-+32+=+0
.
Can we factor 32 into two terms that are 4 apart? 4 * 8 = 32, so we have:
%28y%2B8%29%28y-4%29=0
.
So we have to solutions: y = -8 and y = 4.
.
Checking y=-8, we have:
%28y%2B5%29+=+-8%2B5+=+-3
%28y-1%29+=+-8-1+=+-9
%28y%2B5%29%28y-1%29+=+%28-3%29%28-9%29+=+27
Check.
.
Checking for y+=+4, we have:
%28y%2B5%29+=+4%2B5+=+9
%28y-1%29+=+4-1+=+3
%28y%2B5%29%28y-1%29+=+%283%29%289%29+=+27
Check.
Done.