m-61m^2-11m+30 eching

$$m - 61 m ^ { 2 } - 11 m + 30$$

Omil

$$-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-10m ni olish uchun m va -11m ni birlashtirish.

$$factor(-10m-61m^{2}+30)$$

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.

$$-61m^{2}-10m+30=0$$

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.

$$m=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

-10 kvadratini chiqarish.

$$m=\frac{-\left(-10\right)±\sqrt{100-4\left(-61\right)\times 30}}{2\left(-61\right)}$$

-4 ni -61 marotabaga ko'paytirish.

$$m=\frac{-\left(-10\right)±\sqrt{100+244\times 30}}{2\left(-61\right)}$$

244 ni 30 marotabaga ko'paytirish.

$$m=\frac{-\left(-10\right)±\sqrt{100+7320}}{2\left(-61\right)}$$

100 ni 7320 ga qo'shish.

$$m=\frac{-\left(-10\right)±\sqrt{7420}}{2\left(-61\right)}$$

7420 ning kvadrat ildizini chiqarish.

$$m=\frac{-\left(-10\right)±2\sqrt{1855}}{2\left(-61\right)}$$

-10 ning teskarisi 10 ga teng.

$$m=\frac{10±2\sqrt{1855}}{2\left(-61\right)}$$

2 ni -61 marotabaga ko'paytirish.

$$m=\frac{10±2\sqrt{1855}}{-122}$$

m=\frac{10±2\sqrt{1855}}{-122} tenglamasini yeching, bunda ± musbat. 10 ni 2\sqrt{1855} ga qo'shish.

$$m=\frac{2\sqrt{1855}+10}{-122}$$

10+2\sqrt{1855} ni -122 ga bo'lish.

$$m=\frac{-\sqrt{1855}-5}{61}$$

m=\frac{10±2\sqrt{1855}}{-122} tenglamasini yeching, bunda ± manfiy. 10 dan 2\sqrt{1855} ni ayirish.

$$m=\frac{10-2\sqrt{1855}}{-122}$$

10-2\sqrt{1855} ni -122 ga bo'lish.

$$m=\frac{\sqrt{1855}-5}{61}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-5-\sqrt{1855}}{61} ga va x_{2} uchun \frac{-5+\sqrt{1855}}{61} ga bo‘ling.

$$-61m^{2}-10m+30=-61\left(m-\frac{-\sqrt{1855}-5}{61}\right)\left(m-\frac{\sqrt{1855}-5}{61}\right)$$

Baholash

$$30-10m-61m^{2}$$

Yechim qadamlari

-10m ni olish uchun m va -11m ni birlashtirish.

$$-10m-61m^{2}+30$$