Make n the subject of the formula
E=√x(n-x)/n-1
It's hard to see just what you meant. I'll assume you meant
E=√(x(n-x)/(n-1))
Then that gives
E^2 = x(n-x)/(n-1)
(n-1)E^2 = x(n-x)
E^2n - E^2 = xn - x^2
(E^2-x)n = E^2-x^2
n = (E^2-x^2)/(E^2-x)
If I parsed it wrong, maybe you could either (a)
use some parentheses to clear things up, and then
(b) follow similar steps on your own to arrive at the desired result.
A=E^2-x^2/E^2-x
To make n the subject of the formula E = √[x(n-x)/(n-1)], we can follow the steps below:
Step 1: Square both sides of the equation to get rid of the square root:
E^2 = [x(n-x)/(n-1)]
Step 2: Multiply both sides of the equation by (n-1) to eliminate the denominator:
E^2(n-1) = x(n-x)
Step 3: Expand both sides of the equation:
E^2n - E^2 = xn - x^2
Step 4: Rearrange the terms by moving xn and E^2n to one side of the equation:
xn + E^2n = x^2 + E^2
Step 5: Factor out n on the left side of the equation:
n(x + E^2) = x^2 + E^2
Step 6: Divide both sides of the equation by (x + E^2) to isolate n:
n = (x^2 + E^2)/(x + E^2)
Therefore, the formula with n as the subject is:
n = (x^2 + E^2)/(x + E^2)
To make "n" the subject of the formula E=√x(n-x)/n-1, we want to isolate "n" on one side of the equation.
Here are the steps to make "n" the subject of the formula:
Step 1: Multiply both sides of the equation by n-1 to eliminate the denominator:
(n-1) * E = √x(n-x)
Step 2: Square both sides of the equation to eliminate the square root on the right side:
(n-1)^2 * E^2 = x(n-x)
Step 3: Expand the equation on the left side:
(n^2 - 2n + 1) * E^2 = x(n-x)
Step 4: Distribute E^2:
n^2E^2 - 2nE^2 + E^2 = x(n-x)
Step 5: Expand the equation on the right side:
n^2E^2 - 2nE^2 + E^2 = xn - x^2
Step 6: Rearrange the equation to get all terms on one side:
n^2E^2 - xn + x^2 - 2nE^2 + E^2 = 0
Step 7: Combine like terms:
(E^2 - 2E^2)n + (x^2 - xn) + E^2 = 0
Step 8: Combine the terms with "n":
(-E^2)n + x^2 - xn + E^2 = 0
Step 9: Bring the "n" terms together:
(-E^2)n - xn = - x^2 + E^2
Step 10: Factor out "n":
n(-E^2 - x) = - x^2 + E^2
Finally, to get "n" as the subject, divide both sides of the equation by (-E^2 - x):
n = (- x^2 + E^2) / (-E^2 - x)
Therefore, "n" is equal to (- x^2 + E^2) / (-E^2 - x).