Question 887857
 find exact solutions.
{{{X - 5sqrt(x) - 24 = 0}}}
add 5sqrt(x) to both sides
{{{(x - 24)}}} = {{{5sqrt(x)}}}
Square both sides
{{{(x - 24)^2}}} = {{{25x}}}
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 - 5sqrt(9) - 24 = 0}}}
9 - 15 - 24 does not = 0, not a solution
\and x = 64
{{{64 - 5sqrt(64) - 24 = 0}}}
64 - 5(8) - 24 = 0; only good solution is x = 64
:
:
{{{sqrt(6+2n)- 2 = 2}}}
Add 2 to both sides
{{{sqrt(6+2n)= 4}}}
square both sides
6 + 2n = 16
2n = 16 - 6
2n = 10
n = 5
:"
Check solution in original equation
{{{sqrt(6+2(5))- 2 = 2}}}
{{{sqrt(16)- 2 = 2}}}
4 - 2 = 2, a good solution