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Beliebt Algebra >

completesquare 4x^2-4x+5

Lösung

vervollständige das quadrat

4 x^{2} - 4 x + 5

Lösung

4 (x - \frac{1}{2})^{2} + 4

Schritte zur Lösung

4 x^{2} - 4 x + 5

Schreibe

4 x^{2} - 4 x + 5

in dieser Form:

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

Klammere aus

4

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

2 a = - 1 : a = - \frac{1}{2}

Addiere und subtrahiere

(- \frac{1}{2})^{2}

4 (x^{2} - x + \frac{5}{4} + (- \frac{1}{2})^{2} - (- \frac{1}{2})^{2})

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

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

4 ((x - \frac{1}{2})^{2} + \frac{5}{4} - (- \frac{1}{2})^{2})

Vereinfache

4 (x - \frac{1}{2})^{2} + 4

Graph

Beliebte Beispiele

u^{2} = 20

-0.5x^2+36x-522=0

- 0.5 x^{2} + 36 x - 522 = 0

2 x^{2} + 40 x = - 72

0=-810a+a^2+256064.9

0 = - 810 a + a^{2} + 256064.9

completesquare x^2+12x+3=0

co m pl e t es q u a re x^{2} + 12 x + 3 = 0