01375x^3-11707x^2+52978x-23667 eching

$$01375 { x }^{ 3 } -11707 { x }^{ 2 } +52978x-23667$$

Baholash

$$-11707x^{2}+52978x-23667$$

Yechim qadamlari

0 hosil qilish uchun 0 va 1375 ni ko'paytirish.

$$0x^{3}-11707x^{2}+52978x-23667$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$0-11707x^{2}+52978x-23667$$

-23667 olish uchun 0 dan 23667 ni ayirish.

$$-23667-11707x^{2}+52978x$$

Omil

$$-11707\left(x-\frac{26489-4\sqrt{26537347}}{11707}\right)\left(x-\frac{4\sqrt{26537347}+26489}{11707}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 1375 ni ko'paytirish.

$$factor(0x^{3}-11707x^{2}+52978x-23667)$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$factor(0-11707x^{2}+52978x-23667)$$

-23667 olish uchun 0 dan 23667 ni ayirish.

$$factor(-23667-11707x^{2}+52978x)$$

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.

$$-11707x^{2}+52978x-23667=0$$

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.

$$x=\frac{-52978±\sqrt{52978^{2}-4\left(-11707\right)\left(-23667\right)}}{2\left(-11707\right)}$$

52978 kvadratini chiqarish.

$$x=\frac{-52978±\sqrt{2806668484-4\left(-11707\right)\left(-23667\right)}}{2\left(-11707\right)}$$

-4 ni -11707 marotabaga ko'paytirish.

$$x=\frac{-52978±\sqrt{2806668484+46828\left(-23667\right)}}{2\left(-11707\right)}$$

46828 ni -23667 marotabaga ko'paytirish.

$$x=\frac{-52978±\sqrt{2806668484-1108278276}}{2\left(-11707\right)}$$

2806668484 ni -1108278276 ga qo'shish.

$$x=\frac{-52978±\sqrt{1698390208}}{2\left(-11707\right)}$$

1698390208 ning kvadrat ildizini chiqarish.

$$x=\frac{-52978±8\sqrt{26537347}}{2\left(-11707\right)}$$

2 ni -11707 marotabaga ko'paytirish.

$$x=\frac{-52978±8\sqrt{26537347}}{-23414}$$

x=\frac{-52978±8\sqrt{26537347}}{-23414} tenglamasini yeching, bunda ± musbat. -52978 ni 8\sqrt{26537347} ga qo'shish.

$$x=\frac{8\sqrt{26537347}-52978}{-23414}$$

-52978+8\sqrt{26537347} ni -23414 ga bo'lish.

$$x=\frac{26489-4\sqrt{26537347}}{11707}$$

x=\frac{-52978±8\sqrt{26537347}}{-23414} tenglamasini yeching, bunda ± manfiy. -52978 dan 8\sqrt{26537347} ni ayirish.

$$x=\frac{-8\sqrt{26537347}-52978}{-23414}$$

-52978-8\sqrt{26537347} ni -23414 ga bo'lish.

$$x=\frac{4\sqrt{26537347}+26489}{11707}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{26489-4\sqrt{26537347}}{11707} ga va x_{2} uchun \frac{26489+4\sqrt{26537347}}{11707} ga bo‘ling.

$$-11707x^{2}+52978x-23667=-11707\left(x-\frac{26489-4\sqrt{26537347}}{11707}\right)\left(x-\frac{4\sqrt{26537347}+26489}{11707}\right)$$