Solve the following
I am not sure if I did this correct
(n-5)^2= 20
n-5=+/- 20
n=5+/- sqrt 20
Thanks
yes on the final answer. On the second line, you forgot to type sqrt before 20.
You can reduce it some....sqrt20= sqrt(4*5)= 2 sqrt5
Thanks Bobpursley
To solve the equation (n-5)^2 = 20, you want to isolate the variable n.
1. Start by expanding the square on the left-hand side of the equation: (n-5)(n-5) = 20.
This gives you: n^2 - 10n + 25 = 20.
2. Next, move the constant term (in this case, 20) to the right-hand side of the equation: n^2 - 10n + 25 - 20 = 0.
Simplifying this expression gives you: n^2 - 10n + 5 = 0.
3. Now, you can use the quadratic formula to solve for n: n = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = 1, b = -10, and c = 5.
4. Plug in these values into the quadratic formula:
n = (-(-10) ± √((-10)^2 - 4 * 1 * 5)) / (2 * 1).
5. Simplify the quadratic formula:
n = (10 ± √(100 - 20)) / 2.
n = (10 ± √80) / 2.
6. Simplify the square root of 80:
√80 = √(16 * 5) = 4√5.
7. Substitute this value back into n:
n = (10 ± 4√5) / 2.
8. Simplify the expression inside the parentheses:
n = (5 ± 2√5).
Therefore, the solutions to the equation (n-5)^2 = 20 are n = 5 + 2√5 and n = 5 - 2√5.