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Beliebt Algebra >

completesquare 4x^2+12x+37

Lösung

vervollständige das quadrat

4 x^{2} + 12 x + 37

Lösung

4 (x + \frac{3}{2})^{2} + 28

Schritte zur Lösung

4 x^{2} + 12 x + 37

Schreibe

4 x^{2} + 12 x + 37

in dieser Form:

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

Klammere aus

4

4 (x^{2} + 3 x + \frac{37}{4})

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

Addiere und subtrahiere

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

4 (x^{2} + 3 x + \frac{37}{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}

4 ((x + \frac{3}{2})^{2} + \frac{37}{4} - (\frac{3}{2})^{2})

Vereinfache

4 (x + \frac{3}{2})^{2} + 28

Graph

Beliebte Beispiele

7. 3^{2} + b^{2} = 1 3^{2}

4 k^{2} - 7 = 29

6t^2+6t+14=sqrt(2)

6 t^{2} + 6 t + 14 = 2

0 = 40 x - 4.9 x^{2}

m^{2} = 5 m - 6