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
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) (Show Source):
You can put this solution on YOUR website! this is where it gets confusing:
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:
Then we can use a property of square roots, , to split apart the two factors:
Now we can simplify square root of the perfect square:
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:
Now the 2's cancel leaving:
You can put this solution on YOUR website! Ok, you are good up to: Now you factor the 124 under the radical into 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:, so we get the next step: or Notice that we can factor out a 2 in the numerator and also in the denominator. or Cancel the 2's to leave you with: