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Beliebt Algebra >

completesquare 5x^2-15x+1

Lösung

vervollständige das quadrat

5 x^{2} - 15 x + 1

Lösung

5 (x - \frac{3}{2})^{2} - \frac{41}{4}

Schritte zur Lösung

5 x^{2} - 15 x + 1

Schreibe

5 x^{2} - 15 x + 1

in dieser Form:

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

Klammere aus

5

5 (x^{2} - 3 x + \frac{1}{5})

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

Addiere und subtrahiere

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

5 (x^{2} - 3 x + \frac{1}{5} + (- \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}

5 ((x - \frac{3}{2})^{2} + \frac{1}{5} - (- \frac{3}{2})^{2})

Vereinfache

5 (x - \frac{3}{2})^{2} - \frac{41}{4}

Graph

Beliebte Beispiele

(0.5-x)(1.5*10^{-5})=x^2

(0.5 - x) (1.5 \cdot 1 0^{- 5}) = x^{2}

(2 x - 5) (x + 4) = 0

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

16 x^{2} + 36 = - 48 x

y = - \frac{1}{20} y^{2}