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Beliebt Algebra >

completesquare x^2-7x+8

Lösung

vervollständige das quadrat

x^{2} - 7 x + 8

Lösung

(x - \frac{7}{2})^{2} - \frac{17}{4}

Schritte zur Lösung

x^{2} - 7 x + 8

Schreibe

x^{2} - 7 x + 8

in dieser Form:

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

2 a = - 7 : a = - \frac{7}{2}

Addiere und subtrahiere

(- \frac{7}{2})^{2}

x^{2} - 7 x + 8 + (- \frac{7}{2})^{2} - (- \frac{7}{2})^{2}

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

x^{2} - 7 x + (- \frac{7}{2})^{2} = (x - \frac{7}{2})^{2}

(x - \frac{7}{2})^{2} + 8 - (- \frac{7}{2})^{2}

Vereinfache

(x - \frac{7}{2})^{2} - \frac{17}{4}

Graph

Beliebte Beispiele

k^{2} - 18 k + 8 = - 9

7 x^{2} + 8 = 15

5 x^{2} - 12 x = 0

k (2 k + 5) = 3

- 10 x - 47 = - x^{2} + 1