3x^2-19x-18 eching

$$3 { x }^{ 2 } -19x-18$$

Omil

$$3\left(x-\frac{19-\sqrt{577}}{6}\right)\left(x-\frac{\sqrt{577}+19}{6}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$3x^{2}-19x-18=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}-4\times 3\left(-18\right)}}{2\times 3}$$

-19 kvadratini chiqarish.

$$x=\frac{-\left(-19\right)±\sqrt{361-4\times 3\left(-18\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-19\right)±\sqrt{361-12\left(-18\right)}}{2\times 3}$$

-12 ni -18 marotabaga ko'paytirish.

$$x=\frac{-\left(-19\right)±\sqrt{361+216}}{2\times 3}$$

361 ni 216 ga qo'shish.

$$x=\frac{-\left(-19\right)±\sqrt{577}}{2\times 3}$$

-19 ning teskarisi 19 ga teng.

$$x=\frac{19±\sqrt{577}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{19±\sqrt{577}}{6}$$

x=\frac{19±\sqrt{577}}{6} tenglamasini yeching, bunda ± musbat. 19 ni \sqrt{577} ga qo'shish.

$$x=\frac{\sqrt{577}+19}{6}$$

x=\frac{19±\sqrt{577}}{6} tenglamasini yeching, bunda ± manfiy. 19 dan \sqrt{577} ni ayirish.

$$x=\frac{19-\sqrt{577}}{6}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{19+\sqrt{577}}{6} ga va x_{2} uchun \frac{19-\sqrt{577}}{6} ga bo‘ling.

$$3x^{2}-19x-18=3\left(x-\frac{\sqrt{577}+19}{6}\right)\left(x-\frac{19-\sqrt{577}}{6}\right)$$

Baholash

$$3x^{2}-19x-18$$