x^2-x/9=2/15 eching

$$\frac { x ^ { 2 } - x } { 9 } = \frac { 2 } { 15 }$$

x uchun yechish

$$x=\frac{\sqrt{145}}{10}+\frac{1}{2}\approx 1,704159458$$

$$x=-\frac{\sqrt{145}}{10}+\frac{1}{2}\approx -0,704159458$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafini 9 ga ko‘paytiring.

$$x^{2}-x=\frac{2}{15}\times 9$$

\frac{6}{5} hosil qilish uchun \frac{2}{15} va 9 ni ko'paytirish.

$$x^{2}-x=\frac{6}{5}$$

Ikkala tarafdan \frac{6}{5} ni ayirish.

$$x^{2}-x-\frac{6}{5}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va -\frac{6}{5} ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-\frac{6}{5}\right)}}{2}$$

-4 ni -\frac{6}{5} marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+\frac{24}{5}}}{2}$$

1 ni \frac{24}{5} ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{\frac{29}{5}}}{2}$$

\frac{29}{5} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±\frac{\sqrt{145}}{5}}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\frac{\sqrt{145}}{5}}{2}$$

x=\frac{1±\frac{\sqrt{145}}{5}}{2} tenglamasini yeching, bunda ± musbat. 1 ni \frac{\sqrt{145}}{5} ga qo'shish.

$$x=\frac{\frac{\sqrt{145}}{5}+1}{2}$$

1+\frac{\sqrt{145}}{5} ni 2 ga bo'lish.

$$x=\frac{\sqrt{145}}{10}+\frac{1}{2}$$

x=\frac{1±\frac{\sqrt{145}}{5}}{2} tenglamasini yeching, bunda ± manfiy. 1 dan \frac{\sqrt{145}}{5} ni ayirish.

$$x=\frac{-\frac{\sqrt{145}}{5}+1}{2}$$

1-\frac{\sqrt{145}}{5} ni 2 ga bo'lish.

$$x=-\frac{\sqrt{145}}{10}+\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{145}}{10}+\frac{1}{2} x=-\frac{\sqrt{145}}{10}+\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafini 9 ga ko‘paytiring.

$$x^{2}-x=\frac{2}{15}\times 9$$

\frac{6}{5} hosil qilish uchun \frac{2}{15} va 9 ni ko'paytirish.

$$x^{2}-x=\frac{6}{5}$$

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

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{6}{5}+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=\frac{6}{5}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{6}{5} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-x+\frac{1}{4}=\frac{29}{20}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{29}{20}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{29}{20}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{145}}{10} x-\frac{1}{2}=-\frac{\sqrt{145}}{10}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{145}}{10}+\frac{1}{2} x=-\frac{\sqrt{145}}{10}+\frac{1}{2}$$