SOLUTION: 27X^2/25 = 1/3

Algebra ->  Radicals -> SOLUTION: 27X^2/25 = 1/3      Log On


   

Question 396535: 27X^2/25 = 1/3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
27X%5E2%2F25+=+1%2F3
First let's eliminate the fraction by multiplying both sides by 25:
27X%5E2+=+25%2F3
Dividing both sides by 27 isolates the base, x, and its exponent, 2:
X%5E2+=+25%2F81
Now we can find the square root of each side:
sqrt%28X%5E2%29+=+sqrt%2825%2F81%29
On the left side we get not "x" but abs%28x%29. This is so because a square root is supposed to be positive but we do not know if x is positive. Using absolute value like this ensures that we get a positive square root.
abs%28X%29+=+sqrt%2825%2F81%29
On the right side we can use a property of radicals, root%28a%2C+p%29%2Froot%28a%2C+q%29+=+root%28a%2C+p%2Fq%29, to split the square root of a fraction into a fraction of the square roots of the numerator and denominator:
abs%28X%29+=+sqrt%2825%29%2Fsqrt%2881%29
which simplifies to:
abs%28x%29+=+5%2F9
Solving the absolute value equation we get:
x+=+5%2F9 or x+=+%28-5%29%2F9
These are both solutions to your equation.