SOLUTION: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant un

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant un      Log On


   

Question 297684: I understand how to use the quadratic formula when i'm asked to solve an problem that's straight forward like: x^2+8x+15=0, i can figure out that the answer is {-2/3,4}. I cant understand how to solve the following problem using the quadratic formula:
z^2/1=z/5+6/5
I'm not sure if it's because it involves fractions and i just get really nervous but i'm not sure how to go about solving this problem...
Found 3 solutions by Fombitz, Alan3354, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
z%5E2%2F1=z%2F5%2B6%2F5+
z%5E2-z%2F5-6%2F5=0
You can multiply by the LCD to get rid of the fractions, in this case by 5.
5z%5E2-z-6=0
Then a=5, b=-1, c=-6.
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
z+=+%281+%2B-+sqrt%28+1-4%2A5%2A%28-6%29+%29%29%2F%282%2A5%29+
z+=+%281+%2B-+sqrt%28+121+%29%29%2F%2810%29+
z+=+%281+%2B-+11%29%2F%2810%29+
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Or you can just move forward with the fractions.
z%5E2%2F1=z%2F5%2B6%2F5
z%5E2-z%2F5-6%2F5=0
a=1, b=-1%2F5, c=-6%2F5.
z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25-4%2A1%2A%28-6%2F5%29+%29%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25%2B24%2F5%29+%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+1%2F25%2B120%2F25%29+%29%2F2+
z+=+%281%2F5+%2B-+sqrt%28+121%2F25%29+%29%2F2+
z+=+%281%2F5+%2B-+11%2F5%29+%2F2+
z+=+%281%2F5%29%281+%2B-+11%29%2F2+
z+=+%281+%2B-+11%29%2F10+
You'll get to the same place.
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z=-10%2F10=highlight%28-1%29 and z=12%2F10=highlight%286%2F5%29
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+graph%28+300%2C+300%2C+-3%2C+3%2C+-3%2C3%2C+x%5E2-x%2F5-6%2F5%29+

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
z^2/1=z/5+6/5
Step 1, eliminate fractions.
Multiply thru by 5
5z^2 = z + 6
5z%5E2+-+z+-+6+=+0

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
This one can be factored too once you get it in the right form.
z=-1 and 6/5
First multiply through by 5
5z^2=z+6
5z^-z-6=0
We need factors of -30 which add up to -1
-6 and 5
5z^2-6z+5z-6=0
rearrange
5z^2+5z-6z-6
5z*(z+1)-6(z+1)=0
(5z-6)*(z+1)=0
Now the quadratic formula with the form 5z^2-x-6=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation az%5E2%2Bbz%2Bc=0 (in our case 5z%5E2%2B-1z%2B-6+=+0) has the following solutons:

z%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=%28-1%29%5E2-4%2A5%2A-6=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+121+%29%29%2F2%5Ca.

z%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C5+=+1.2
z%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C5+=+-1

Quadratic expression 5z%5E2%2B-1z%2B-6 can be factored:
5z%5E2%2B-1z%2B-6+=+5%28z-1.2%29%2A%28z--1%29
Again, the answer is: 1.2, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-1%2Ax%2B-6+%29