1+x+x(1+x)=36 eching

$$1 + x + x ( 1 + x ) = 36$$

x uchun yechish

$$x=-7$$

$$x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1+x+x+x^{2}=36$$

2x ni olish uchun x va x ni birlashtirish.

$$1+2x+x^{2}=36$$

Ikkala tarafdan 36 ni ayirish.

$$1+2x+x^{2}-36=0$$

-35 olish uchun 1 dan 36 ni ayirish.

$$-35+2x+x^{2}=0$$

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.

$$x^{2}+2x-35=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -35 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-35\right)}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-35\right)}}{2}$$

-4 ni -35 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+140}}{2}$$

4 ni 140 ga qo'shish.

$$x=\frac{-2±\sqrt{144}}{2}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±12}{2}$$

x=\frac{-2±12}{2} tenglamasini yeching, bunda ± musbat. -2 ni 12 ga qo'shish.

$$x=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$x=5$$

x=\frac{-2±12}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 12 ni ayirish.

$$x=-\frac{14}{2}$$

-14 ni 2 ga bo'lish.

$$x=-7$$

Tenglama yechildi.

$$x=5 x=-7$$

Kvadratni yakunlash bo'yicha qadamlar

x ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$1+x+x+x^{2}=36$$

2x ni olish uchun x va x ni birlashtirish.

$$1+2x+x^{2}=36$$

Ikkala tarafdan 1 ni ayirish.

$$2x+x^{2}=36-1$$

35 olish uchun 36 dan 1 ni ayirish.

$$2x+x^{2}=35$$

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

$$x^{2}+2x=35$$

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

$$x^{2}+2x+1^{2}=35+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=35+1$$

35 ni 1 ga qo'shish.

$$x^{2}+2x+1=36$$

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

$$\left(x+1\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$x+1=6 x+1=-6$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=5 x=-7$$