2pir^2+36pir-357=0

Lösung

2 π r^{2} + 36 π r - 357 = 0

r = \frac{- 36 π + 1296 π ^{2} + 2856 π}{4 π}, r = \frac{- 36 π - 1296 π ^{2} + 2856 π}{4 π}

Dezimale

r = 2.73960 \dots, r = - 20.73960 \dots

Schritte zur Lösung

2 π r^{2} + 36 π r - 357 = 0

Löse mit der quadratischen Formel

r_{1, 2} = \frac{- 36 π \pm ( 36 π ) ^{2} - 4 \cdot 2 π ( - 357 )}{2 \cdot 2 π}

(36 π)^{2} - 4 \cdot 2 π (- 357) = 1296 π^{2} + 2856 π

r_{1, 2} = \frac{- 36 π \pm 1296 π ^{2} + 2856 π}{2 \cdot 2 π}

Trenne die Lösungen

r_{1} = \frac{- 36 π + 1296 π ^{2} + 2856 π}{2 \cdot 2 π}, r_{2} = \frac{- 36 π - 1296 π ^{2} + 2856 π}{2 \cdot 2 π}

r = \frac{- 36 π + 1296 π ^{2} + 2856 π}{2 \cdot 2 π} : \frac{- 36 π + 1296 π ^{2} + 2856 π}{4 π}

r = \frac{- 36 π - 1296 π ^{2} + 2856 π}{2 \cdot 2 π} : \frac{- 36 π - 1296 π ^{2} + 2856 π}{4 π}

Die Lösungen für die quadratische Gleichung sind:

r = \frac{- 36 π + 1296 π ^{2} + 2856 π}{4 π}, r = \frac{- 36 π - 1296 π ^{2} + 2856 π}{4 π}

- 3 x^{2} - 6 x + 21 = 6 x + 8

4 x^{2} = - 8 x - 1

so l v e f or x, x^{2} + k (4 x + 17) = 0

so l v e f or x, x^{2} - 2 x + 3 = 0

(x + 1)^{2} = e^{2}