5x^2=8x-16/5 eching

$$5 x ^ { 2 } = 8 x - \frac { 16 } { 5 }$$

x uchun yechish

$$x=\frac{4}{5}=0,8$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 8x ni ayirish.

$$5x^{2}-8x=-\frac{16}{5}$$

\frac{16}{5} ni ikki tarafga qo’shing.

$$5x^{2}-8x+\frac{16}{5}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -8 ni b va \frac{16}{5} ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 5\times \frac{16}{5}}}{2\times 5}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 5\times \frac{16}{5}}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-20\times \frac{16}{5}}}{2\times 5}$$

-20 ni \frac{16}{5} marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-64}}{2\times 5}$$

64 ni -64 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{0}}{2\times 5}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{-8}{2\times 5}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{8}{10}$$

\frac{8}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{4}{5}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 8x ni ayirish.

$$5x^{2}-8x=-\frac{16}{5}$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-8x}{5}=-\frac{\frac{16}{5}}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{8}{5}x=-\frac{\frac{16}{5}}{5}$$

-\frac{16}{5} ni 5 ga bo'lish.

$$x^{2}-\frac{8}{5}x=-\frac{16}{25}$$

-\frac{8}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{4}{5} olish uchun. Keyin, -\frac{4}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{8}{5}x+\left(-\frac{4}{5}\right)^{2}=-\frac{16}{25}+\left(-\frac{4}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{4}{5} kvadratini chiqarish.

$$x^{2}-\frac{8}{5}x+\frac{16}{25}=\frac{-16+16}{25}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{16}{25} ni \frac{16}{25} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{8}{5}x+\frac{16}{25}=0$$

x^{2}-\frac{8}{5}x+\frac{16}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{4}{5}\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{4}{5}\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-\frac{4}{5}=0 x-\frac{4}{5}=0$$

\frac{4}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{4}{5} x=\frac{4}{5}$$

Tenglama yechildi. Yechimlar bir xil.

$$x=\frac{4}{5}$$