18x^2+600-230x eching

$$18 { x }^{ 2 } +600-230x$$

Omil

$$18\left(x-\frac{115-5\sqrt{97}}{18}\right)\left(x-\frac{5\sqrt{97}+115}{18}\right)$$

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.

$$18x^{2}-230x+600=0$$

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.

$$x=\frac{-\left(-230\right)±\sqrt{\left(-230\right)^{2}-4\times 18\times 600}}{2\times 18}$$

-230 kvadratini chiqarish.

$$x=\frac{-\left(-230\right)±\sqrt{52900-4\times 18\times 600}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-230\right)±\sqrt{52900-72\times 600}}{2\times 18}$$

-72 ni 600 marotabaga ko'paytirish.

$$x=\frac{-\left(-230\right)±\sqrt{52900-43200}}{2\times 18}$$

52900 ni -43200 ga qo'shish.

$$x=\frac{-\left(-230\right)±\sqrt{9700}}{2\times 18}$$

9700 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-230\right)±10\sqrt{97}}{2\times 18}$$

-230 ning teskarisi 230 ga teng.

$$x=\frac{230±10\sqrt{97}}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{230±10\sqrt{97}}{36}$$

x=\frac{230±10\sqrt{97}}{36} tenglamasini yeching, bunda ± musbat. 230 ni 10\sqrt{97} ga qo'shish.

$$x=\frac{10\sqrt{97}+230}{36}$$

230+10\sqrt{97} ni 36 ga bo'lish.

$$x=\frac{5\sqrt{97}+115}{18}$$

x=\frac{230±10\sqrt{97}}{36} tenglamasini yeching, bunda ± manfiy. 230 dan 10\sqrt{97} ni ayirish.

$$x=\frac{230-10\sqrt{97}}{36}$$

230-10\sqrt{97} ni 36 ga bo'lish.

$$x=\frac{115-5\sqrt{97}}{18}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{115+5\sqrt{97}}{18} ga va x_{2} uchun \frac{115-5\sqrt{97}}{18} ga bo‘ling.

$$18x^{2}-230x+600=18\left(x-\frac{5\sqrt{97}+115}{18}\right)\left(x-\frac{115-5\sqrt{97}}{18}\right)$$

Baholash

$$18x^{2}-230x+600$$