(0.1-z)z=0 eching

$$( 0.1 - z ) z = 0$$

z uchun yechish

$$z=0$$

$$z=0,1$$

Faktorlash qadamlari

0,1-z ga z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0,1z-z^{2}=0$$

z omili.

$$z\left(0,1-z\right)=0$$

Tenglamani yechish uchun z=0 va 0,1-z=0 ni yeching.

$$z=0 z=\frac{1}{10}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0.1-z ga z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0.1z-z^{2}=0$$

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.

$$-z^{2}+\frac{1}{10}z=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, \frac{1}{10} ni b va 0 ni c bilan almashtiring.

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

\left(\frac{1}{10}\right)^{2} ning kvadrat ildizini chiqarish.

$$z=\frac{-\frac{1}{10}±\frac{1}{10}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$z=\frac{-\frac{1}{10}±\frac{1}{10}}{-2}$$

z=\frac{-\frac{1}{10}±\frac{1}{10}}{-2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{10} ni \frac{1}{10} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$z=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$z=0$$

z=\frac{-\frac{1}{10}±\frac{1}{10}}{-2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{1}{10} ni -\frac{1}{10} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$z=-\frac{\frac{1}{5}}{-2}$$

-\frac{1}{5} ni -2 ga bo'lish.

$$z=\frac{1}{10}$$

Tenglama yechildi.

$$z=0 z=\frac{1}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

0.1-z ga z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$0.1z-z^{2}=0$$

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

$$-z^{2}+\frac{1}{10}z=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-z^{2}+\frac{1}{10}z}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$z^{2}+\frac{\frac{1}{10}}{-1}z=\frac{0}{-1}$$

\frac{1}{10} ni -1 ga bo'lish.

$$z^{2}-\frac{1}{10}z=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$z^{2}-\frac{1}{10}z=0$$

-\frac{1}{10} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{20} olish uchun. Keyin, -\frac{1}{20} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$z^{2}-\frac{1}{10}z+\left(-\frac{1}{20}\right)^{2}=\left(-\frac{1}{20}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{20} kvadratini chiqarish.

$$z^{2}-\frac{1}{10}z+\frac{1}{400}=\frac{1}{400}$$

z^{2}-\frac{1}{10}z+\frac{1}{400} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(z-\frac{1}{20}\right)^{2}=\frac{1}{400}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(z-\frac{1}{20}\right)^{2}}=\sqrt{\frac{1}{400}}$$

Qisqartirish.

$$z-\frac{1}{20}=\frac{1}{20} z-\frac{1}{20}=-\frac{1}{20}$$

\frac{1}{20} ni tenglamaning ikkala tarafiga qo'shish.

$$z=\frac{1}{10} z=0$$