-9x^2+18x+68= eching

$$- 9 x ^ { 2 } + 18 x + 68 =$$

Omil

$$-9\left(x-\left(-\frac{\sqrt{77}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{77}}{3}+1\right)\right)$$

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.

$$-9x^{2}+18x+68=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-9\right)\times 68}}{2\left(-9\right)}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-9\right)\times 68}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+36\times 68}}{2\left(-9\right)}$$

36 ni 68 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+2448}}{2\left(-9\right)}$$

324 ni 2448 ga qo'shish.

$$x=\frac{-18±\sqrt{2772}}{2\left(-9\right)}$$

2772 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±6\sqrt{77}}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{-18±6\sqrt{77}}{-18}$$

x=\frac{-18±6\sqrt{77}}{-18} tenglamasini yeching, bunda ± musbat. -18 ni 6\sqrt{77} ga qo'shish.

$$x=\frac{6\sqrt{77}-18}{-18}$$

-18+6\sqrt{77} ni -18 ga bo'lish.

$$x=-\frac{\sqrt{77}}{3}+1$$

x=\frac{-18±6\sqrt{77}}{-18} tenglamasini yeching, bunda ± manfiy. -18 dan 6\sqrt{77} ni ayirish.

$$x=\frac{-6\sqrt{77}-18}{-18}$$

-18-6\sqrt{77} ni -18 ga bo'lish.

$$x=\frac{\sqrt{77}}{3}+1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 1-\frac{\sqrt{77}}{3} ga va x_{2} uchun 1+\frac{\sqrt{77}}{3} ga bo‘ling.

$$-9x^{2}+18x+68=-9\left(x-\left(-\frac{\sqrt{77}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{77}}{3}+1\right)\right)$$

Baholash

$$68+18x-9x^{2}$$