n2-15n+100
well, 100 = 20*5
oops. That helps with n^2-15n-100 = 0
Your equation has no real solutions, since the discriminant is negative: 225-400 < 0
To simplify the expression n^2 - 15n + 100, you can factor or use the quadratic formula.
1. Factoring:
To factorize the equation, we need to find two numbers that multiply to give 100 and add up to -15 (the coefficient of n). In this case, the numbers are -10 and -5 because -10 * -5 = 100 and -10 + -5 = -15.
Therefore, we can rewrite the equation as (n - 10)(n - 5).
2. Quadratic Formula:
If factoring is not feasible, you can always use the quadratic formula to find the solutions for n. The quadratic formula is given by:
n = (-b ± √(b^2 - 4ac)) / 2a
In our equation, n^2 - 15n + 100, a = 1, b = -15, and c = 100.
Plugging in these values into the quadratic formula, we get:
n = (-(-15) ± √((-15)^2 - 4(1)(100))) / (2(1))
= (15 ± √(225 - 400)) / 2
= (15 ± √(-175)) / 2
Since we have a negative number under the square root (√-175), the expression has no real solutions. The result is a complex number.