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Beliebt Algebra >

completesquare 5x-x^2

Lösung

vervollständige das quadrat

5 x - x^{2}

Lösung

- (x - \frac{5}{2})^{2} + \frac{25}{4}

Schritte zur Lösung

5 x - x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- x^{2} + 5 x

Schreibe

- x^{2} + 5 x

in dieser Form:

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

Klammere aus

- 1

- (x^{2} - 5 x)

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

Addiere und subtrahiere

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

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

Vereinfache

- (x - \frac{5}{2})^{2} + \frac{25}{4}

Graph

Beliebte Beispiele

0.32x^2-1.2x+1=0

0.32 x^{2} - 1.2 x + 1 = 0

ax^2+(a+b)x+b=0

a x^{2} + (a + b) x + b = 0

x + 3 = 39 - x^{2}

y = y (4 - y)

x^{2} - 10 x = - 22