5x(3-4x)=15x-4x eching

$$5 x ( 3 - 4 x ) = 15 x - 4 x$$

x uchun yechish

$$x=\frac{1}{5}=0,2$$

$$x=0$$

Faktorlash qadamlari

5x ga 3-4x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$15x-20x^{2}=15x-4x$$

11x ni olish uchun 15x va -4x ni birlashtirish.

$$15x-20x^{2}=11x$$

Ikkala tarafdan 11x ni ayirish.

$$15x-20x^{2}-11x=0$$

4x ni olish uchun 15x va -11x ni birlashtirish.

$$4x-20x^{2}=0$$

x omili.

$$x\left(4-20x\right)=0$$

Tenglamani yechish uchun x=0 va 4-20x=0 ni yeching.

$$x=0 x=\frac{1}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

5x ga 3-4x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$15x-20x^{2}=15x-4x$$

11x ni olish uchun 15x va -4x ni birlashtirish.

$$15x-20x^{2}=11x$$

Ikkala tarafdan 11x ni ayirish.

$$15x-20x^{2}-11x=0$$

4x ni olish uchun 15x va -11x ni birlashtirish.

$$4x-20x^{2}=0$$

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.

$$-20x^{2}+4x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -20 ni a, 4 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}}}{2\left(-20\right)}$$

4^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-4±4}{-40}$$

x=\frac{-4±4}{-40} tenglamasini yeching, bunda ± musbat. -4 ni 4 ga qo'shish.

$$x=\frac{0}{-40}$$

0 ni -40 ga bo'lish.

$$x=0$$

x=\frac{-4±4}{-40} tenglamasini yeching, bunda ± manfiy. -4 dan 4 ni ayirish.

$$x=-\frac{8}{-40}$$

\frac{-8}{-40} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

$$x=0 x=\frac{1}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

5x ga 3-4x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$15x-20x^{2}=15x-4x$$

11x ni olish uchun 15x va -4x ni birlashtirish.

$$15x-20x^{2}=11x$$

Ikkala tarafdan 11x ni ayirish.

$$15x-20x^{2}-11x=0$$

4x ni olish uchun 15x va -11x ni birlashtirish.

$$4x-20x^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-20x^{2}+4x=0$$

Ikki tarafini -20 ga bo‘ling.

$$\frac{-20x^{2}+4x}{-20}=\frac{0}{-20}$$

-20 ga bo'lish -20 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{4}{-20}x=\frac{0}{-20}$$

\frac{4}{-20} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{5}x=\frac{0}{-20}$$

0 ni -20 ga bo'lish.

$$x^{2}-\frac{1}{5}x=0$$

-\frac{1}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{10} olish uchun. Keyin, -\frac{1}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{5}x+\left(-\frac{1}{10}\right)^{2}=\left(-\frac{1}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{10} kvadratini chiqarish.

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

x^{2}-\frac{1}{5}x+\frac{1}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{10}\right)^{2}=\frac{1}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{10}\right)^{2}}=\sqrt{\frac{1}{100}}$$

Qisqartirish.

$$x-\frac{1}{10}=\frac{1}{10} x-\frac{1}{10}=-\frac{1}{10}$$

\frac{1}{10} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{5} x=0$$