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Beliebt Algebra >

completesquare 12x^2-60x+5

Lösung

vervollständige das quadrat

12 x^{2} - 60 x + 5

Lösung

12 (x - \frac{5}{2})^{2} - 70

Schritte zur Lösung

12 x^{2} - 60 x + 5

Schreibe

12 x^{2} - 60 x + 5

in dieser Form:

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

Klammere aus

12

12 (x^{2} - 5 x + \frac{5}{12})

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

Addiere und subtrahiere

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

12 (x^{2} - 5 x + \frac{5}{12} + (- \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}

12 ((x - \frac{5}{2})^{2} + \frac{5}{12} - (- \frac{5}{2})^{2})

Vereinfache

12 (x - \frac{5}{2})^{2} - 70

Graph

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