(x+2)(x+4)+39=3(x+x+6) eching

$$( x + 2 ) ( x + 4 ) + 39 = 3 ( x + x + 6 )$$

x uchun yechish (complex solution)

$$x=-\sqrt{29}i\approx -0-5,385164807i$$

$$x=\sqrt{29}i\approx 5,385164807i$$

Kvadrat ildizini topish bo'yicha qadamlar

x+2 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+6x+8+39=3\left(x+x+6\right)$$

47 olish uchun 8 va 39'ni qo'shing.

$$x^{2}+6x+47=3\left(x+x+6\right)$$

2x ni olish uchun x va x ni birlashtirish.

$$x^{2}+6x+47=3\left(2x+6\right)$$

3 ga 2x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+6x+47=6x+18$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}+6x+47-6x=18$$

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

$$x^{2}+47=18$$

Ikkala tarafdan 47 ni ayirish.

$$x^{2}=18-47$$

-29 olish uchun 18 dan 47 ni ayirish.

$$x^{2}=-29$$

Tenglama yechildi.

$$x=\sqrt{29}i x=-\sqrt{29}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+2 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+6x+8+39=3\left(x+x+6\right)$$

47 olish uchun 8 va 39'ni qo'shing.

$$x^{2}+6x+47=3\left(x+x+6\right)$$

2x ni olish uchun x va x ni birlashtirish.

$$x^{2}+6x+47=3\left(2x+6\right)$$

3 ga 2x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+6x+47=6x+18$$

Ikkala tarafdan 6x ni ayirish.

$$x^{2}+6x+47-6x=18$$

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

$$x^{2}+47=18$$

Ikkala tarafdan 18 ni ayirish.

$$x^{2}+47-18=0$$

29 olish uchun 47 dan 18 ni ayirish.

$$x^{2}+29=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va 29 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 29}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 29}}{2}$$

-4 ni 29 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-116}}{2}$$

-116 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{29}i}{2}$$

x=\frac{0±2\sqrt{29}i}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{29}i$$

x=\frac{0±2\sqrt{29}i}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{29}i$$

Tenglama yechildi.

$$x=\sqrt{29}i x=-\sqrt{29}i$$