-0125x^3+15x^2-x-12 eching

$$-0125 { x }^{ 3 } +15 { x }^{ 2 } -x-12$$

Baholash

$$15x^{2}-x-12$$

Yechim qadamlari

0 hosil qilish uchun 0 va 125 ni ko'paytirish.

$$0x^{3}+15x^{2}-x-12$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$0+15x^{2}-x-12$$

-12 olish uchun 0 dan 12 ni ayirish.

$$-12+15x^{2}-x$$

Omil

$$15\left(x-\frac{1-\sqrt{721}}{30}\right)\left(x-\frac{\sqrt{721}+1}{30}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 125 ni ko'paytirish.

$$factor(0x^{3}+15x^{2}-x-12)$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$factor(0+15x^{2}-x-12)$$

-12 olish uchun 0 dan 12 ni ayirish.

$$factor(-12+15x^{2}-x)$$

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.

$$15x^{2}-x-12=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 15\left(-12\right)}}{2\times 15}$$

-4 ni 15 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-60\left(-12\right)}}{2\times 15}$$

-60 ni -12 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+720}}{2\times 15}$$

1 ni 720 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{721}}{2\times 15}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{721}}{2\times 15}$$

2 ni 15 marotabaga ko'paytirish.

$$x=\frac{1±\sqrt{721}}{30}$$

x=\frac{1±\sqrt{721}}{30} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{721} ga qo'shish.

$$x=\frac{\sqrt{721}+1}{30}$$

x=\frac{1±\sqrt{721}}{30} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{721} ni ayirish.

$$x=\frac{1-\sqrt{721}}{30}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{721}}{30} ga va x_{2} uchun \frac{1-\sqrt{721}}{30} ga bo‘ling.

$$15x^{2}-x-12=15\left(x-\frac{\sqrt{721}+1}{30}\right)\left(x-\frac{1-\sqrt{721}}{30}\right)$$