completesquare b^2+19b

Lösung

vervollständige das quadrat

b^{2} + 19 b

(b + \frac{19}{2})^{2} - \frac{361}{4}

Schritte zur Lösung

b^{2} + 19 b

Schreibe

b^{2} + 19 b

in dieser Form:

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

2 a = 19 : a = \frac{19}{2}

Addiere und subtrahiere

(\frac{19}{2})^{2}

b^{2} + 19 b + (\frac{19}{2})^{2} - (\frac{19}{2})^{2}

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

b^{2} + 19 b + (\frac{19}{2})^{2} = (b + \frac{19}{2})^{2}

(b + \frac{19}{2})^{2} - (\frac{19}{2})^{2}

Vereinfache

(b + \frac{19}{2})^{2} - \frac{361}{4}

co m pl e t es q u a re x^{2} - 6 x = 0

so l v e f or x, \frac{x ^{2}}{4} + \frac{y ^{2}}{9} - \frac{z ^{2}}{25} = 0

so l v e f or x, z = x^{2} - 4 x y + y^{2} - 6 y

so l v e f or x, x^{2} + y^{2} - 12 x + 14 y + 85 = 0

(x^{2} - 10 x + 21) = 0