30x^2+100x-280000 eching

$$30 { x }^{ 2 } +100x-280000$$

Omil

$$30\left(x-\frac{-5\sqrt{3361}-5}{3}\right)\left(x-\frac{5\sqrt{3361}-5}{3}\right)$$

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.

$$30x^{2}+100x-280000=0$$

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.

$$x=\frac{-100±\sqrt{100^{2}-4\times 30\left(-280000\right)}}{2\times 30}$$

100 kvadratini chiqarish.

$$x=\frac{-100±\sqrt{10000-4\times 30\left(-280000\right)}}{2\times 30}$$

-4 ni 30 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000-120\left(-280000\right)}}{2\times 30}$$

-120 ni -280000 marotabaga ko'paytirish.

$$x=\frac{-100±\sqrt{10000+33600000}}{2\times 30}$$

10000 ni 33600000 ga qo'shish.

$$x=\frac{-100±\sqrt{33610000}}{2\times 30}$$

33610000 ning kvadrat ildizini chiqarish.

$$x=\frac{-100±100\sqrt{3361}}{2\times 30}$$

2 ni 30 marotabaga ko'paytirish.

$$x=\frac{-100±100\sqrt{3361}}{60}$$

x=\frac{-100±100\sqrt{3361}}{60} tenglamasini yeching, bunda ± musbat. -100 ni 100\sqrt{3361} ga qo'shish.

$$x=\frac{100\sqrt{3361}-100}{60}$$

-100+100\sqrt{3361} ni 60 ga bo'lish.

$$x=\frac{5\sqrt{3361}-5}{3}$$

x=\frac{-100±100\sqrt{3361}}{60} tenglamasini yeching, bunda ± manfiy. -100 dan 100\sqrt{3361} ni ayirish.

$$x=\frac{-100\sqrt{3361}-100}{60}$$

-100-100\sqrt{3361} ni 60 ga bo'lish.

$$x=\frac{-5\sqrt{3361}-5}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-5+5\sqrt{3361}}{3} ga va x_{2} uchun \frac{-5-5\sqrt{3361}}{3} ga bo‘ling.

$$30x^{2}+100x-280000=30\left(x-\frac{5\sqrt{3361}-5}{3}\right)\left(x-\frac{-5\sqrt{3361}-5}{3}\right)$$

Baholash

$$30x^{2}+100x-280000$$