5w^2-40w-50 eching

$$5 w ^ { 2 } - 40 w - 50$$

Omil

$$5\left(w-\left(4-\sqrt{26}\right)\right)\left(w-\left(\sqrt{26}+4\right)\right)$$

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.

$$5w^{2}-40w-50=0$$

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.

$$w=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 5\left(-50\right)}}{2\times 5}$$

-40 kvadratini chiqarish.

$$w=\frac{-\left(-40\right)±\sqrt{1600-4\times 5\left(-50\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$w=\frac{-\left(-40\right)±\sqrt{1600-20\left(-50\right)}}{2\times 5}$$

-20 ni -50 marotabaga ko'paytirish.

$$w=\frac{-\left(-40\right)±\sqrt{1600+1000}}{2\times 5}$$

1600 ni 1000 ga qo'shish.

$$w=\frac{-\left(-40\right)±\sqrt{2600}}{2\times 5}$$

2600 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-40\right)±10\sqrt{26}}{2\times 5}$$

-40 ning teskarisi 40 ga teng.

$$w=\frac{40±10\sqrt{26}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$w=\frac{40±10\sqrt{26}}{10}$$

w=\frac{40±10\sqrt{26}}{10} tenglamasini yeching, bunda ± musbat. 40 ni 10\sqrt{26} ga qo'shish.

$$w=\frac{10\sqrt{26}+40}{10}$$

40+10\sqrt{26} ni 10 ga bo'lish.

$$w=\sqrt{26}+4$$

w=\frac{40±10\sqrt{26}}{10} tenglamasini yeching, bunda ± manfiy. 40 dan 10\sqrt{26} ni ayirish.

$$w=\frac{40-10\sqrt{26}}{10}$$

40-10\sqrt{26} ni 10 ga bo'lish.

$$w=4-\sqrt{26}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 4+\sqrt{26} ga va x_{2} uchun 4-\sqrt{26} ga bo‘ling.

$$5w^{2}-40w-50=5\left(w-\left(\sqrt{26}+4\right)\right)\left(w-\left(4-\sqrt{26}\right)\right)$$

Baholash

$$5\left(w^{2}-8w-10\right)$$