SOLUTION: Hi, I am solving quadratic equation by formula -b sqrt (b^2-4ac)/2(a) I solved down to the bottom and am not sure what to do, would you show me the next step? I think its is re

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I am solving quadratic equation by formula -b sqrt (b^2-4ac)/2(a) I solved down to the bottom and am not sure what to do, would you show me the next step? I think its is re      Log On


   

Question 409320: Hi, I am solving quadratic equation by formula -b sqrt (b^2-4ac)/2(a)
I solved down to the bottom and am not sure what to do, would you show me the next step? I think its is reducing. How to do that?
Thanks
4y(y+1)=1
4y^2+4y=1
4y^2+4y-1=1-1
4y^2+4y-1=0
-4 +- sqrt ((4)^2-4(4)(-1)/((2(4))
-4 +- sqrt (16-(-16))/(8)
-4 +- sqrt (32)/(8) What do I do now?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You are perfect up to:
y+=+%28-4+%2B-+sqrt+%2832%29%29%2F8
Next we simplify the square root. Square roots of perfect squares are fairly simple to simplify. 32 is not a perfect square so it is not as easy to simplify this square root. But 32 does have a perfect square factor:
y+=+%28-4+%2B-+sqrt+%2816%2A2%29%29%2F8
Now we can use a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to split the square root into the product of the square roots of the factors:
y+=+%28-4+%2B-+sqrt+%2816%29%2Asqrt%282%29%29%2F8
The square root of the perfect square simplifies:
y+=+%28-4+%2B-+4%2Asqrt%282%29%29%2F8
Now we can reduce the fraction. Reducing fractions involves canceling common factors. So we need to factor the numerator and denominator:
y+=+%284%28-1+%2B-+sqrt%282%29%29%29%2F%284%2A2%29
as you can see, there is a common factor we can cancel:
y+=+%28cross%284%29%28-1+%2B-+sqrt%282%29%29%29%2F%28cross%284%29%2A2%29
leaving:
y+=+%28-1+%2B-+sqrt%282%29%29%2F2
This is as far as we can go with the "+-". We can write this in "long form":
y+=+%28-1+%2B+sqrt%282%29%29%2F2 or y+=+%28-1+-+sqrt%282%29%29%2F2