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Beliebt Algebra >

completesquare x^2+3x+1

Lösung

vervollständige das quadrat

x^{2} + 3 x + 1

Lösung

(x + \frac{3}{2})^{2} - \frac{5}{4}

Schritte zur Lösung

x^{2} + 3 x + 1

Schreibe

x^{2} + 3 x + 1

in dieser Form:

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

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

Addiere und subtrahiere

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

x^{2} + 3 x + 1 + (\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} + 1 - (\frac{3}{2})^{2}

Vereinfache

(x + \frac{3}{2})^{2} - \frac{5}{4}

Graph

Beliebte Beispiele

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

n^{2} - 2 n = 15

(x-1/4)(x+1/4)= 3/16

(x - \frac{1}{4}) (x + \frac{1}{4}) = \frac{3}{16}

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

w^{2} - 8 w + 7 = - 3