SOLUTION: can you help me here? a number is increased by the square root of this result is less than the square root of half the number is 3. Find the number.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: can you help me here? a number is increased by the square root of this result is less than the square root of half the number is 3. Find the number.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 931131: can you help me here? a number is increased by the square root of this result is less than the square root of half the number is 3. Find the number.
Answer by ptfile(81) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number
A number is increased by the square root of this result is less than the square root of half the number is 3.
√x-√(x/2)=3
√ x=√(x/2)+3
(√x)^2=(√(x/2)+3)^2
x=x/2+6√(x/2)+9
0=-x+x/2+6√(x/2)+9
0=-x/2+(6√(x/2))(√(2/2)+9
0=-x/2+6√(2x/2)/2+18/2
0=-x+6√2x+18
(x-18)^2=(6√2x)^2
x^2-36x+324=72x
x^2-36x+324-72x=0
x^2-108x+324=0
Use Quadratic formula to solve for x
x=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x=+%28108+%2B-+sqrt%28+11664-1296+%29%29%2F%282%29+
x=+%28108+%2B-+sqrt%28+10368+%29%29%2F%282%29+
x = 104.91168824543142175686079407155 or 105
or
x = 3.08831175456857824313920592845 or 3
Substitute x for 105
√(105)-√((105)/2)= 3
10 - 7 = 3
3 = 3
Substitute x for 3
√(3)-√((3)/2)= 3
2 - 1 = 3
1 = 3
The number is 105.