3x^2+18x+9 eching

$$3 x ^ { 2 } + 18 x + 9$$

Omil

$$3\left(x-\left(-\sqrt{6}-3\right)\right)\left(x-\left(\sqrt{6}-3\right)\right)$$

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.

$$3x^{2}+18x+9=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 3\times 9}}{2\times 3}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\times 3\times 9}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-12\times 9}}{2\times 3}$$

-12 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-108}}{2\times 3}$$

324 ni -108 ga qo'shish.

$$x=\frac{-18±\sqrt{216}}{2\times 3}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±6\sqrt{6}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-18±6\sqrt{6}}{6}$$

x=\frac{-18±6\sqrt{6}}{6} tenglamasini yeching, bunda ± musbat. -18 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}-18}{6}$$

-18+6\sqrt{6} ni 6 ga bo'lish.

$$x=\sqrt{6}-3$$

x=\frac{-18±6\sqrt{6}}{6} tenglamasini yeching, bunda ± manfiy. -18 dan 6\sqrt{6} ni ayirish.

$$x=\frac{-6\sqrt{6}-18}{6}$$

-18-6\sqrt{6} ni 6 ga bo'lish.

$$x=-\sqrt{6}-3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -3+\sqrt{6} ga va x_{2} uchun -3-\sqrt{6} ga bo‘ling.

$$3x^{2}+18x+9=3\left(x-\left(\sqrt{6}-3\right)\right)\left(x-\left(-\sqrt{6}-3\right)\right)$$

Baholash

$$3\left(x^{2}+6x+3\right)$$