9x^2+18x+1 eching

$$9 x ^ { 2 } + 18 x + 1$$

Omil

$$9\left(x-\left(-\frac{2\sqrt{2}}{3}-1\right)\right)\left(x-\left(\frac{2\sqrt{2}}{3}-1\right)\right)$$

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.

$$9x^{2}+18x+1=0$$

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.

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

18 kvadratini chiqarish.

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

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-36}}{2\times 9}$$

324 ni -36 ga qo'shish.

$$x=\frac{-18±\sqrt{288}}{2\times 9}$$

288 ning kvadrat ildizini chiqarish.

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

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{-18±12\sqrt{2}}{18}$$

x=\frac{-18±12\sqrt{2}}{18} tenglamasini yeching, bunda ± musbat. -18 ni 12\sqrt{2} ga qo'shish.

$$x=\frac{12\sqrt{2}-18}{18}$$

-18+12\sqrt{2} ni 18 ga bo'lish.

$$x=\frac{2\sqrt{2}}{3}-1$$

x=\frac{-18±12\sqrt{2}}{18} tenglamasini yeching, bunda ± manfiy. -18 dan 12\sqrt{2} ni ayirish.

$$x=\frac{-12\sqrt{2}-18}{18}$$

-18-12\sqrt{2} ni 18 ga bo'lish.

$$x=-\frac{2\sqrt{2}}{3}-1$$

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

$$9x^{2}+18x+1=9\left(x-\left(\frac{2\sqrt{2}}{3}-1\right)\right)\left(x-\left(-\frac{2\sqrt{2}}{3}-1\right)\right)$$

Baholash

$$9x^{2}+18x+1$$