(-9c^2-5c+7)+(3c+9) eching

$$( - 9 c ^ { 2 } - 5 c + 7 ) + ( 3 c + 9 )$$

Baholash

$$16-2c-9c^{2}$$

Yechim qadamlari

-2c ni olish uchun -5c va 3c ni birlashtirish.

$$-9c^{2}-2c+7+9$$

16 olish uchun 7 va 9'ni qo'shing.

$$-9c^{2}-2c+16$$

Omil

$$-9\left(c-\frac{-\sqrt{145}-1}{9}\right)\left(c-\frac{\sqrt{145}-1}{9}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-2c ni olish uchun -5c va 3c ni birlashtirish.

$$factor(-9c^{2}-2c+7+9)$$

16 olish uchun 7 va 9'ni qo'shing.

$$factor(-9c^{2}-2c+16)$$

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.

$$-9c^{2}-2c+16=0$$

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.

$$c=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-9\right)\times 16}}{2\left(-9\right)}$$

-2 kvadratini chiqarish.

$$c=\frac{-\left(-2\right)±\sqrt{4-4\left(-9\right)\times 16}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$c=\frac{-\left(-2\right)±\sqrt{4+36\times 16}}{2\left(-9\right)}$$

36 ni 16 marotabaga ko'paytirish.

$$c=\frac{-\left(-2\right)±\sqrt{4+576}}{2\left(-9\right)}$$

4 ni 576 ga qo'shish.

$$c=\frac{-\left(-2\right)±\sqrt{580}}{2\left(-9\right)}$$

580 ning kvadrat ildizini chiqarish.

$$c=\frac{-\left(-2\right)±2\sqrt{145}}{2\left(-9\right)}$$

-2 ning teskarisi 2 ga teng.

$$c=\frac{2±2\sqrt{145}}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$c=\frac{2±2\sqrt{145}}{-18}$$

c=\frac{2±2\sqrt{145}}{-18} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{145} ga qo'shish.

$$c=\frac{2\sqrt{145}+2}{-18}$$

2+2\sqrt{145} ni -18 ga bo'lish.

$$c=\frac{-\sqrt{145}-1}{9}$$

c=\frac{2±2\sqrt{145}}{-18} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{145} ni ayirish.

$$c=\frac{2-2\sqrt{145}}{-18}$$

2-2\sqrt{145} ni -18 ga bo'lish.

$$c=\frac{\sqrt{145}-1}{9}$$

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{145}}{9} ga va x_{2} uchun \frac{-1+\sqrt{145}}{9} ga bo‘ling.

$$-9c^{2}-2c+16=-9\left(c-\frac{-\sqrt{145}-1}{9}\right)\left(c-\frac{\sqrt{145}-1}{9}\right)$$