completesquare 2x^2-5x-3

Lösung

vervollständige das quadrat

2 x^{2} - 5 x - 3

2 (x - \frac{5}{4})^{2} - \frac{49}{8}

Schritte zur Lösung

2 x^{2} - 5 x - 3

Schreibe

2 x^{2} - 5 x - 3

in dieser Form:

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

Klammere aus

2

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

2 a = - \frac{5}{2} : a = - \frac{5}{4}

Addiere und subtrahiere

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

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

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

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

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

Vereinfache

2 (x - \frac{5}{4})^{2} - \frac{49}{8}

co m pl e t es q u a re u^{2} + 16 u

\frac{x ^{2}}{3} - 3 = 0

5 x^{2} + 2 x - 9 = 0

z^{2} + 21 = 10 z

so l v e f or x, z = 10 - x^{2} - y^{2}