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Beliebt Algebra >

completesquare 4-3x-x^2

Lösung

vervollständige das quadrat

4 - 3 x - x^{2}

Lösung

- (x + \frac{3}{2})^{2} + \frac{25}{4}

Schritte zur Lösung

4 - 3 x - x^{2}

Schreibe in der Standard Form

a x^{2} + b x + c

- x^{2} - 3 x + 4

Schreibe

- x^{2} - 3 x + 4

in dieser Form:

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

Klammere aus

- 1

- (x^{2} + 3 x - 4)

2 a = 3 : a = \frac{3}{2}

Addiere und subtrahiere

(\frac{3}{2})^{2}

- (x^{2} + 3 x - 4 + (\frac{3}{2})^{2} - (\frac{3}{2})^{2})

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

x^{2} + 3 x + (\frac{3}{2})^{2} = (x + \frac{3}{2})^{2}

- ((x + \frac{3}{2})^{2} - 4 - (\frac{3}{2})^{2})

Vereinfache

- (x + \frac{3}{2})^{2} + \frac{25}{4}

Graph

Beliebte Beispiele

3 m^{2} - 9 m = 30

3 x^{2} - 5 x = 3 x + 5

15 = x^{2} - 1

x^{2} = x - 3

2 x^{2} - 1 = 4