2m-14quaddiv1/m^2-3m-28 eching

$$2 m - 14 \quad \div \frac { 1 } { m ^ { 2 } - 3 m - 28 }$$

Baholash

$$392+44m-14m^{2}$$

Yechim qadamlari

14 ni \frac{1}{m^{2}-3m-28} ga bo'lish 14 ga k'paytirish \frac{1}{m^{2}-3m-28} ga qaytarish.

$$2m-14\left(m^{2}-3m-28\right)$$

14 ga m^{2}-3m-28 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2m-\left(14m^{2}-42m-392\right)$$

14m^{2}-42m-392 teskarisini topish uchun har birining teskarisini toping.

$$2m-14m^{2}+42m+392$$

44m ni olish uchun 2m va 42m ni birlashtirish.

$$44m-14m^{2}+392$$

Omil

$$-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

14 ni \frac{1}{m^{2}-3m-28} ga bo'lish 14 ga k'paytirish \frac{1}{m^{2}-3m-28} ga qaytarish.

$$factor(2m-14\left(m^{2}-3m-28\right))$$

14 ga m^{2}-3m-28 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$factor(2m-\left(14m^{2}-42m-392\right))$$

14m^{2}-42m-392 teskarisini topish uchun har birining teskarisini toping.

$$factor(2m-14m^{2}+42m+392)$$

44m ni olish uchun 2m va 42m ni birlashtirish.

$$factor(44m-14m^{2}+392)$$

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.

$$-14m^{2}+44m+392=0$$

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.

$$m=\frac{-44±\sqrt{44^{2}-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

44 kvadratini chiqarish.

$$m=\frac{-44±\sqrt{1936-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

-4 ni -14 marotabaga ko'paytirish.

$$m=\frac{-44±\sqrt{1936+56\times 392}}{2\left(-14\right)}$$

56 ni 392 marotabaga ko'paytirish.

$$m=\frac{-44±\sqrt{1936+21952}}{2\left(-14\right)}$$

1936 ni 21952 ga qo'shish.

$$m=\frac{-44±\sqrt{23888}}{2\left(-14\right)}$$

23888 ning kvadrat ildizini chiqarish.

$$m=\frac{-44±4\sqrt{1493}}{2\left(-14\right)}$$

2 ni -14 marotabaga ko'paytirish.

$$m=\frac{-44±4\sqrt{1493}}{-28}$$

m=\frac{-44±4\sqrt{1493}}{-28} tenglamasini yeching, bunda ± musbat. -44 ni 4\sqrt{1493} ga qo'shish.

$$m=\frac{4\sqrt{1493}-44}{-28}$$

-44+4\sqrt{1493} ni -28 ga bo'lish.

$$m=\frac{11-\sqrt{1493}}{7}$$

m=\frac{-44±4\sqrt{1493}}{-28} tenglamasini yeching, bunda ± manfiy. -44 dan 4\sqrt{1493} ni ayirish.

$$m=\frac{-4\sqrt{1493}-44}{-28}$$

-44-4\sqrt{1493} ni -28 ga bo'lish.

$$m=\frac{\sqrt{1493}+11}{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{11-\sqrt{1493}}{7} ga va x_{2} uchun \frac{11+\sqrt{1493}}{7} ga bo‘ling.

$$-14m^{2}+44m+392=-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$