pq-Formel für Gleichung x^2-6x=9

Question

wie bringt man die Gleichung x^2-6x=9 in die Pq formel

Answer 1

$$ x^2 -6x = 9 \quad | -9 $$

$$ x^2-6x-9=0 $$

Anwenden der PQ Formel

$$ p=-6 \quad q=-9 $$

$$ \frac{-p}{2}\pm \sqrt{\left(\frac{p}{2}\right)^2-q} $$

$$ \frac{--6}{2}\pm \sqrt{\left(\frac{-6}{2}\right)^2-(-9)} $$

$$ x_1 = -1.2426... \quad x_2 =7.2426 $$

~plot~ x^2-6x-9 ~plot~



Hope this helps!

Answer 2

x^2-6x = 9 | -9

x^2 -6x -9=0 ->pq-Formel

x_1.2= 3± √ (9 +9)

x_1.2= 3± √ 18 

x_1.2= 3± 3 √2