(x)=2/3x(2x+9)-5x+1 eching

$$( x ) = \frac { 2 } { 3 } x ( 2 x + 9 ) - 5 x + 1$$

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{3}i}{2}\approx -0-0,866025404i$$

$$x=\frac{\sqrt{3}i}{2}\approx 0,866025404i$$

Kvadrat ildizini topish bo'yicha qadamlar

\frac{2}{3}x ga 2x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x=\frac{2}{3}x\times 2x+\frac{2}{3}x\times 9-5x+1$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x=\frac{2}{3}x^{2}\times 2+\frac{2}{3}x\times 9-5x+1$$

\frac{2}{3}\times 2 ni yagona kasrga aylantiring.

$$x=\frac{2\times 2}{3}x^{2}+\frac{2}{3}x\times 9-5x+1$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$x=\frac{4}{3}x^{2}+\frac{2}{3}x\times 9-5x+1$$

\frac{2}{3}\times 9 ni yagona kasrga aylantiring.

$$x=\frac{4}{3}x^{2}+\frac{2\times 9}{3}x-5x+1$$

18 hosil qilish uchun 2 va 9 ni ko'paytirish.

$$x=\frac{4}{3}x^{2}+\frac{18}{3}x-5x+1$$

6 ni olish uchun 18 ni 3 ga bo‘ling.

$$x=\frac{4}{3}x^{2}+6x-5x+1$$

x ni olish uchun 6x va -5x ni birlashtirish.

$$x=\frac{4}{3}x^{2}+x+1$$

Ikkala tarafdan \frac{4}{3}x^{2} ni ayirish.

$$x-\frac{4}{3}x^{2}=x+1$$

Ikkala tarafdan x ni ayirish.

$$x-\frac{4}{3}x^{2}-x=1$$

0 ni olish uchun x va -x ni birlashtirish.

$$-\frac{4}{3}x^{2}=1$$

Ikki tarafini -\frac{3}{4} va teskari kasri -\frac{4}{3} ga ko‘paytiring.

$$x^{2}=1\left(-\frac{3}{4}\right)$$

-\frac{3}{4} hosil qilish uchun 1 va -\frac{3}{4} ni ko'paytirish.

$$x^{2}=-\frac{3}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\frac{2}{3}x ga 2x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x=\frac{2}{3}x\times 2x+\frac{2}{3}x\times 9-5x+1$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x=\frac{2}{3}x^{2}\times 2+\frac{2}{3}x\times 9-5x+1$$

\frac{2}{3}\times 2 ni yagona kasrga aylantiring.

$$x=\frac{2\times 2}{3}x^{2}+\frac{2}{3}x\times 9-5x+1$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$x=\frac{4}{3}x^{2}+\frac{2}{3}x\times 9-5x+1$$

\frac{2}{3}\times 9 ni yagona kasrga aylantiring.

$$x=\frac{4}{3}x^{2}+\frac{2\times 9}{3}x-5x+1$$

18 hosil qilish uchun 2 va 9 ni ko'paytirish.

$$x=\frac{4}{3}x^{2}+\frac{18}{3}x-5x+1$$

6 ni olish uchun 18 ni 3 ga bo‘ling.

$$x=\frac{4}{3}x^{2}+6x-5x+1$$

x ni olish uchun 6x va -5x ni birlashtirish.

$$x=\frac{4}{3}x^{2}+x+1$$

Ikkala tarafdan \frac{4}{3}x^{2} ni ayirish.

$$x-\frac{4}{3}x^{2}=x+1$$

Ikkala tarafdan x ni ayirish.

$$x-\frac{4}{3}x^{2}-x=1$$

0 ni olish uchun x va -x ni birlashtirish.

$$-\frac{4}{3}x^{2}=1$$

Ikkala tarafdan 1 ni ayirish.

$$-\frac{4}{3}x^{2}-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{4}{3} ni a, 0 ni b va -1 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{4}{3}\right)\left(-1\right)}}{2\left(-\frac{4}{3}\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{4}{3}\right)\left(-1\right)}}{2\left(-\frac{4}{3}\right)}$$

-4 ni -\frac{4}{3} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{16}{3}\left(-1\right)}}{2\left(-\frac{4}{3}\right)}$$

\frac{16}{3} ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-\frac{16}{3}}}{2\left(-\frac{4}{3}\right)}$$

-\frac{16}{3} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{4\sqrt{3}i}{3}}{2\left(-\frac{4}{3}\right)}$$

2 ni -\frac{4}{3} marotabaga ko'paytirish.

$$x=\frac{0±\frac{4\sqrt{3}i}{3}}{-\frac{8}{3}}$$

x=\frac{0±\frac{4\sqrt{3}i}{3}}{-\frac{8}{3}} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{\sqrt{3}i}{2}$$

x=\frac{0±\frac{4\sqrt{3}i}{3}}{-\frac{8}{3}} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{\sqrt{3}i}{2}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{3}i}{2} x=\frac{\sqrt{3}i}{2}$$