PQ Formel Rechner - mit Brüchen und Gleichungen

Online Rechner für die PQ Formel. Es können beliebige Gleichungen eingegeben werden welche anschießend in eine für die PQ Formel anwendbare Form umgerechnet werden. Für die Lösung wird hierbei in allen Fällen die PQ Formel angewendet. Die Rechenschritte zur Lösung werden hierbei mit angezeigt.

Beispiele für den PQ-Formel Online Rechner:

$x^2 + 6x + 8$

$x^2 - \frac{2}{3} - 5 = 0$

$-(3x+3)(2x+4)$

$12 x^2 + 1 = 7x$

$\sqrt{3} x^2 + \sqrt{3} = 6x$

Weitere Beispiele findest Du in den PQ Formel Übungsaufgaben

Wie lautet Deine PQ-Formel?

Folgendes wird berechnet:

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Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /homepages/pj-mathe/htdocs/_data/evalmath.class.php on line 384

Deine eingegebene Formel

$x\left(x-5\right) = 8\left(x-4\right)-4$

Klammern ausrechnen, vereinfachen, umschreiben

$x^{2}-5x = 8x-36$

Alle Werte der rechten Seite auf die linke Seite bringen (Nullform)

$x^{2}+\left(-5-8\right)x+36 = 0$

Und das Ganze zusammenfassen

$x^{2}-13x+36 = 0$

Die PQ-Formel zum Berechnen

$x^2-13x+36 = 0$

mit den Werten

$p = -13$ und $q = 36$

einsetzen in die PQ Formel

$x_{1,2}=-{\frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2-q}}$

Einsetzen in die PQ-Formel liefert

$x_{1,2}=-\frac{-13}{2} \pm \sqrt{\left(\frac{-13}2\right)^2-36}$

Nach Möglichkeit $-\frac{p}{2}$ vereinfachen, Quadrat in der Wurzel ausrechnen

$x_{1,2}=\frac{13}{2} \pm \sqrt{\frac{169}{4}-36}$

Wert in der Wurzel ausrechnen

$x_{1,2}=\frac{13}{2}\pm \sqrt{\frac{25}{4}}$

Wurzel ziehen

$x_{1,2}=\frac{13}{2}\pm 2.5$

Als Ergebnis erhält man

$x_{1}=9$

$x_{2}=4$