X berechnen wenn y = 2

Question

Aufgabe:

f(x)=−0,5x²+5x-8

Problem/Ansatz:

Was wäre x, wenn y=2?

Answer 1

−0,5x²+5x-8 = 2

−0,5x²+5x-10 = 0  | *-2

 x²-10x+20 = 0

 x²-10x+25 - 5  = 0

(x-5)^2 = 5

x-5 = ±√5

x = 5 ±√5

Answer 2

-0.5x^2 + 5x - 8 = 2 | -2

-0.5x^2 + 5x - 10 = 0 | :(-0.5)

x^2 - 10x + 20 = 0 | p-q-Formel

 x_1,2 = - \( \frac{-10}{2} \) ± \( \sqrt{(\frac{-10}{2})^{2} - 20 } \)

x_1,2 = 5 ± \( \sqrt{5} \)