4x^2-11x eching

$$4 x ^ { 2 } - 11 x$$

Omil

$$x\left(4x-11\right)$$

Yechim qadamlari

x omili.

$$x\left(4x-11\right)$$

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.

$$4x^{2}-11x=0$$

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.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}}}{2\times 4}$$

\left(-11\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±11}{2\times 4}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±11}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{11±11}{8}$$

x=\frac{11±11}{8} tenglamasini yeching, bunda ± musbat. 11 ni 11 ga qo'shish.

$$x=\frac{22}{8}$$

\frac{22}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{11}{4}$$

x=\frac{11±11}{8} tenglamasini yeching, bunda ± manfiy. 11 dan 11 ni ayirish.

$$x=\frac{0}{8}$$

0 ni 8 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{11}{4} ga va x_{2} uchun 0 ga bo‘ling.

$$4x^{2}-11x=4\left(x-\frac{11}{4}\right)x$$

Umumiy maxrajni topib va suratlarni ayirib \frac{11}{4} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$4x^{2}-11x=4\times \frac{4x-11}{4}x$$

4 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$4x^{2}-11x=\left(4x-11\right)x$$

Baholash

$$x\left(4x-11\right)$$