SOLUTION: Stuck on these quadratic equations! Trying to find exact solutions. X- 5{sqrt}x -24=0 {sqrt}(6+2n)-2=2

Question 887857: Stuck on these quadratic equations!
Trying to find exact solutions.
X- 5{sqrt}x -24=0
{sqrt}(6+2n)-2=2
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
find exact solutions.

add 5sqrt(x) to both sides
=
Square both sides
=
FOIL (x-24)(x-24)
x^2 - 48x + 576 = 25x
x^2 - 48x - 25x + 576 = 0
x^2 - 73x + 576 = 0
You can use the quadratic formula to find x, but this will factor to:
(x-9)(x-64) = 0
two solutions
x = 9
x = 64
when a radical is involved, it's very important to try both solutions in the original equation
x = 9

9 - 15 - 24 does not = 0, not a solution
\and x = 64

64 - 5(8) - 24 = 0; only good solution is x = 64
:
:

Add 2 to both sides

square both sides
6 + 2n = 16
2n = 16 - 6
2n = 10
n = 5
:"
Check solution in original equation

4 - 2 = 2, a good solution
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