SOLUTION: I need help with one part of solution when using the quadratic formula. My textbook does not explain this part. I will list up to where I begin to get confused. Solve: 5x^2-8x-3

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need help with one part of solution when using the quadratic formula. My textbook does not explain this part. I will list up to where I begin to get confused. Solve: 5x^2-8x-3      Log On


   

Question 204020: I need help with one part of solution when using the quadratic formula. My textbook does not explain this part. I will list up to where I begin to get confused.
Solve: 5x^2-8x-3=0
a=5, b=-8. c=-3
-(-8)+/- sqrt(-8)^2-4(5)(-3) divided by 2(5)
8 +/- sqrt64+60 divided by 10
8 +/- sqrt124 divided by 10

this is where it gets confusing:
8+/- sqrt (4) (31) divided by 10
8+/- 2 sqrt31 divided by 10 =2(4+/- sqrt31 divided by (2)(5)
= 2/2 times 4+/- sqrt31 divided by 5 = 4+/-sqrt31 divided by 5
I do not understand what is happening during this part. Please walk me through and explain what is being done and why it is done. thank you
Found 3 solutions by jim_thompson5910, jsmallt9, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll start where you're starting to get confused


x=%288%2B-sqrt%28124%29%29%2F%2810%29 Start with the given equation.


The goal now is to simplify the right side any way we can. It turns out that the square root can be simplified.


x=%288%2B-sqrt%284%2A31%29%29%2F%2810%29 Factor 124 into 4*31. Note: 4*31=124.


Why did we do this? Because when we break up the root, we can take the square root of 4 to get 2...

x=%288%2B-sqrt%284%29%2Asqrt%2831%29%29%2F%2810%29 Break up the square root.


x=%288+%2B-+2%2Asqrt%2831%29%29%2F%2810%29 Take the square root of 4 to get 2.


x=%282%284%2B-sqrt%2831%29%29%29%2F%2810%29 Factor out the GCF 2 from the numerator.


x=%282%284%2B-sqrt%2831%29%29%29%2F%282%2A5%29 Factor the denominator 10 to get 2*5


x=%28highlight%282%29%284%2B-sqrt%2831%29%29%29%2F%28highlight%282%29%2A5%29 Highlight the common terms.


x=%28cross%282%29%284%2B-sqrt%2831%29%29%29%2F%28cross%282%29%2A5%29 Cancel out the common terms.


x=%284%2B-sqrt%2831%29%29%2F5 Simplify


So the solutions are x=%284%2Bsqrt%2831%29%29%2F5 or x=%284-sqrt%2831%29%29%2F5 (since the 'plus/minus' breaks the equation in two).


Note: I showed more steps than you would necessarily show to illustrate what is really going on.

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
this is where it gets confusing:
%288+%2B-+sqrt%28124%29%29%2F10
The next step is simplifying the square root. Simplifying square roots is done by finding perfect square factors of the radicand (the number inside the square root), if possible. The largest perfect square factor in 124 is 4. So we can rewrite 124 as 4*31:
%288+%2B-+sqrt%284%2A31%29%29%2F10
Then we can use a property of square roots, sqrt%28a%2Ab%29+=+sqrt%28a%29%2Asqrt%28b%29, to split apart the two factors:
%288+%2B-+sqrt%284%29%2Asqrt%2831%29%29%2F10
Now we can simplify square root of the perfect square:
%288+%2B-+2%2Asqrt%2831%29%29%2F10
The only thing left to do is reduce the fraction. This is done, as always, by finding common factors which will cancel. In this case 2 is a factor of both the numerator and denominator. So if we factor it out we can cancel them:
%282%284+%2B-+sqrt%2831%29%29%29%2F%282%2A5%29
Now the 2's cancel leaving:
%284+%2B-+sqrt%2831%29%29%2F5

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, you are good up to:
x+=+%288%2B-sqrt%28124%29%29%2F10 Now you factor the 124 under the radical into sqrt%28124%29+=+sqrt%284%2A31%29 and the purpose of this step is to see if the radicand (the quantity under the radical) has any factors that are perfect squares. In this case, there is a factor of 4 which is a perfect square and can be moved out from under the radical by taking its square root, since:sqrt%284%29+=+2, so we get the next step:
x+=+%288%2B2%2Asqrt%2831%29%29%2F10 or x+=+%288-2%2Asqrt%2831%29%29%2F10 Notice that we can factor out a 2 in the numerator and also in the denominator.
x+=+%28cross%282%29%284%2Bsqrt%2831%29%29%29%2Fcross%282%29%285%29 or x+=+%28cross%282%29%284-sqrt%2831%29%29%29%2Fcross%282%29%285%29 Cancel the 2's to leave you with:
highlight%28x+=+%284%2B-sqrt%2831%29%29%2F5%29