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Beliebt Algebra >

completesquare 7+5x-x^2

Lösung

vervollständige das quadrat

7 + 5 x - x^{2}

Lösung

- (x - \frac{5}{2})^{2} + \frac{53}{4}

Schritte zur Lösung

7 + 5 x - x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- x^{2} + 5 x + 7

Schreibe

- x^{2} + 5 x + 7

in dieser Form:

x^{2} + 2 a x + a^{2}

Klammere aus

- 1

- (x^{2} - 5 x - 7)

2 a = - 5 : a = - \frac{5}{2}

Addiere und subtrahiere

(- \frac{5}{2})^{2}

- (x^{2} - 5 x - 7 + (- \frac{5}{2})^{2} - (- \frac{5}{2})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} - 5 x + (- \frac{5}{2})^{2} = (x - \frac{5}{2})^{2}

- ((x - \frac{5}{2})^{2} - 7 - (- \frac{5}{2})^{2})

Vereinfache

- (x - \frac{5}{2})^{2} + \frac{53}{4}

Graph

Beliebte Beispiele

x^{2} - 2 = 3 x - 4

x^2+(2m+5)x+m=0

x^{2} + (2 m + 5) x + m = 0

r^{2} - 9 r = - 8

-3x^2-2x=4-6x^2+1

- 3 x^{2} - 2 x = 4 - 6 x^{2} + 1

- 4 t^{2} - 20 t + 3 = 0