3n^2-14n+5n^2-64 eching

$$3 n ^ { 2 } - 14 n + 5 n ^ { 2 } - 64$$

Omil

$$8\left(n-\frac{7-\sqrt{561}}{8}\right)\left(n-\frac{\sqrt{561}+7}{8}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

8n^{2} ni olish uchun 3n^{2} va 5n^{2} ni birlashtirish.

$$factor(8n^{2}-14n-64)$$

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.

$$8n^{2}-14n-64=0$$

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.

$$n=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 8\left(-64\right)}}{2\times 8}$$

-14 kvadratini chiqarish.

$$n=\frac{-\left(-14\right)±\sqrt{196-4\times 8\left(-64\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$n=\frac{-\left(-14\right)±\sqrt{196-32\left(-64\right)}}{2\times 8}$$

-32 ni -64 marotabaga ko'paytirish.

$$n=\frac{-\left(-14\right)±\sqrt{196+2048}}{2\times 8}$$

196 ni 2048 ga qo'shish.

$$n=\frac{-\left(-14\right)±\sqrt{2244}}{2\times 8}$$

2244 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-14\right)±2\sqrt{561}}{2\times 8}$$

-14 ning teskarisi 14 ga teng.

$$n=\frac{14±2\sqrt{561}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$n=\frac{14±2\sqrt{561}}{16}$$

n=\frac{14±2\sqrt{561}}{16} tenglamasini yeching, bunda ± musbat. 14 ni 2\sqrt{561} ga qo'shish.

$$n=\frac{2\sqrt{561}+14}{16}$$

14+2\sqrt{561} ni 16 ga bo'lish.

$$n=\frac{\sqrt{561}+7}{8}$$

n=\frac{14±2\sqrt{561}}{16} tenglamasini yeching, bunda ± manfiy. 14 dan 2\sqrt{561} ni ayirish.

$$n=\frac{14-2\sqrt{561}}{16}$$

14-2\sqrt{561} ni 16 ga bo'lish.

$$n=\frac{7-\sqrt{561}}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{7+\sqrt{561}}{8} ga va x_{2} uchun \frac{7-\sqrt{561}}{8} ga bo‘ling.

$$8n^{2}-14n-64=8\left(n-\frac{\sqrt{561}+7}{8}\right)\left(n-\frac{7-\sqrt{561}}{8}\right)$$

Baholash

$$8n^{2}-14n-64$$

Yechim qadamlari

8n^{2} ni olish uchun 3n^{2} va 5n^{2} ni birlashtirish.

$$8n^{2}-14n-64$$