SOLUTION: 1/4(8y+4)-17=1/2(4y-8)

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Question 149800This question is from textbook Introductory Algebra
: 1/4(8y+4)-17=1/2(4y-8)This question is from textbook Introductory Algebra

Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
I can't tell if you mean 1%2F%284%288y%2B4%29%29 or %288y%2B4%29%2F4
Parens are cheap - no need to be stingy with them.
I'll assume you mean
%281%2F4%29%288y%2B4%29-17=%281%2F2%29%284y-8%29
%282y%2B1%29+-+17+=+%282y+-+4%29
-16+=+-4
This is not true. So my original assumption on the problem must have been wrong.
Now let's assume you meant
%281%2F%284%288y%2B4%29%29%29-17=%281%2F%282%284y-8%29%29%29
%281%2F%2816%282y%2B1%29%29%29-17=%281%2F%288%28y-2%29%29%29 Multiply by 16
%281%2F%282y%2B1%29%29-272=%282%2F%28y-2%29%29
%281%2F%282y%2B1%29%29-272+-%282%2F%28y-2%29%29=+0 Get a common denominator
%28+%28y-2%29+-272%28y-2%29%282y%2B1%29+-+2%282y%2B1%29+%29+%2F+%28%28y-2%29%282y%2B1%29%29=+0 Don't forget the denominator. We'll need to check the answers we get to make sure they don't result in a 0 in the denominator.
%28+%28y-2%29+-272%28y-2%29%282y%2B1%29+-+2%282y%2B1%29+%29=+0
+y+-+2+-+272%282y%5E2+-3y+-+2%29+-+4y+-+2+=+0+
-544y%5E2+%2B+816y+%2B+544+-3y+-4+=+0
544y%5E2+-813y+-540+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 544x%5E2%2B-813x%2B-540+=+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=%28-813%29%5E2-4%2A544%2A-540=1836009.

Discriminant d=1836009 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--813%2B-sqrt%28+1836009+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-813%29%2Bsqrt%28+1836009+%29%29%2F2%5C544+=+1.99264163228685
x%5B2%5D+=+%28-%28-813%29-sqrt%28+1836009+%29%29%2F2%5C544+=+-0.498156338169206

Quadratic expression 544x%5E2%2B-813x%2B-540 can be factored:
544x%5E2%2B-813x%2B-540+=+544%28x-1.99264163228685%29%2A%28x--0.498156338169206%29
Again, the answer is: 1.99264163228685, -0.498156338169206. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+544%2Ax%5E2%2B-813%2Ax%2B-540+%29


The solutions are 'close to the zeroes' in the original denominator, but not equal