2p^2-2400000p+7000000 eching

$$2 p ^ { 2 } - 2400000 p + 7000000$$

Omil

$$2\left(p-\left(600000-500\sqrt{1439986}\right)\right)\left(p-\left(500\sqrt{1439986}+600000\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$2p^{2}-2400000p+7000000=0$$

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.

$$p=\frac{-\left(-2400000\right)±\sqrt{\left(-2400000\right)^{2}-4\times 2\times 7000000}}{2\times 2}$$

-2400000 kvadratini chiqarish.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-4\times 2\times 7000000}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-8\times 7000000}}{2\times 2}$$

-8 ni 7000000 marotabaga ko'paytirish.

$$p=\frac{-\left(-2400000\right)±\sqrt{5760000000000-56000000}}{2\times 2}$$

5760000000000 ni -56000000 ga qo'shish.

$$p=\frac{-\left(-2400000\right)±\sqrt{5759944000000}}{2\times 2}$$

5759944000000 ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-2400000\right)±2000\sqrt{1439986}}{2\times 2}$$

-2400000 ning teskarisi 2400000 ga teng.

$$p=\frac{2400000±2000\sqrt{1439986}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$p=\frac{2400000±2000\sqrt{1439986}}{4}$$

p=\frac{2400000±2000\sqrt{1439986}}{4} tenglamasini yeching, bunda ± musbat. 2400000 ni 2000\sqrt{1439986} ga qo'shish.

$$p=\frac{2000\sqrt{1439986}+2400000}{4}$$

2400000+2000\sqrt{1439986} ni 4 ga bo'lish.

$$p=500\sqrt{1439986}+600000$$

p=\frac{2400000±2000\sqrt{1439986}}{4} tenglamasini yeching, bunda ± manfiy. 2400000 dan 2000\sqrt{1439986} ni ayirish.

$$p=\frac{2400000-2000\sqrt{1439986}}{4}$$

2400000-2000\sqrt{1439986} ni 4 ga bo'lish.

$$p=600000-500\sqrt{1439986}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 600000+500\sqrt{1439986} ga va x_{2} uchun 600000-500\sqrt{1439986} ga bo‘ling.

$$2p^{2}-2400000p+7000000=2\left(p-\left(500\sqrt{1439986}+600000\right)\right)\left(p-\left(600000-500\sqrt{1439986}\right)\right)$$

Baholash

$$2\left(p^{2}-1200000p+3500000\right)$$