100x^2-20x eching

$$100 x ^ { 2 } - 20 x$$

Omil

$$20x\left(5x-1\right)$$

Yechim qadamlari

20 omili.

$$20\left(5x^{2}-x\right)$$

Hisoblang: 5x^{2}-x. x omili.

$$x\left(5x-1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$20x\left(5x-1\right)$$

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.

$$100x^{2}-20x=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 100}$$

\left(-20\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±20}{2\times 100}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±20}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$x=\frac{20±20}{200}$$

x=\frac{20±20}{200} tenglamasini yeching, bunda ± musbat. 20 ni 20 ga qo'shish.

$$x=\frac{40}{200}$$

\frac{40}{200} ulushini 40 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{5}$$

x=\frac{20±20}{200} tenglamasini yeching, bunda ± manfiy. 20 dan 20 ni ayirish.

$$x=\frac{0}{200}$$

0 ni 200 ga bo'lish.

$$x=0$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1}{5} ga va x_{2} uchun 0 ga bo‘ling.

$$100x^{2}-20x=100\left(x-\frac{1}{5}\right)x$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{5} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$100x^{2}-20x=100\times \frac{5x-1}{5}x$$

100 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$100x^{2}-20x=20\left(5x-1\right)x$$

Baholash

$$20x\left(5x-1\right)$$