b^2+12(5-b)=0 eching

$$b ^ { 2 } + 12 ( 5 - b ) = 0$$

b uchun yechish

$$b=6+2\sqrt{6}i\approx 6+4,898979486i$$

$$b=-2\sqrt{6}i+6\approx 6-4,898979486i$$

Kvadrat tenglamalaridan foydalanish qoidalari

12 ga 5-b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$b^{2}+60-12b=0$$

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.

$$b^{2}-12b+60=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va 60 ni c bilan almashtiring.

$$b=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 60}}{2}$$

-12 kvadratini chiqarish.

$$b=\frac{-\left(-12\right)±\sqrt{144-4\times 60}}{2}$$

-4 ni 60 marotabaga ko'paytirish.

$$b=\frac{-\left(-12\right)±\sqrt{144-240}}{2}$$

144 ni -240 ga qo'shish.

$$b=\frac{-\left(-12\right)±\sqrt{-96}}{2}$$

-96 ning kvadrat ildizini chiqarish.

$$b=\frac{-\left(-12\right)±4\sqrt{6}i}{2}$$

-12 ning teskarisi 12 ga teng.

$$b=\frac{12±4\sqrt{6}i}{2}$$

b=\frac{12±4\sqrt{6}i}{2} tenglamasini yeching, bunda ± musbat. 12 ni 4i\sqrt{6} ga qo'shish.

$$b=\frac{12+4\sqrt{6}i}{2}$$

12+4i\sqrt{6} ni 2 ga bo'lish.

$$b=6+2\sqrt{6}i$$

b=\frac{12±4\sqrt{6}i}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 4i\sqrt{6} ni ayirish.

$$b=\frac{-4\sqrt{6}i+12}{2}$$

12-4i\sqrt{6} ni 2 ga bo'lish.

$$b=-2\sqrt{6}i+6$$

Tenglama yechildi.

$$b=6+2\sqrt{6}i b=-2\sqrt{6}i+6$$

Kvadratni yakunlash bo'yicha qadamlar

12 ga 5-b ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$b^{2}+60-12b=0$$

Ikkala tarafdan 60 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$b^{2}-12b=-60$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$b^{2}-12b+\left(-6\right)^{2}=-60+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$b^{2}-12b+36=-60+36$$

-60 ni 36 ga qo'shish.

$$b^{2}-12b+36=-24$$

b^{2}-12b+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(b-6\right)^{2}=-24$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b-6\right)^{2}}=\sqrt{-24}$$

Qisqartirish.

$$b-6=2\sqrt{6}i b-6=-2\sqrt{6}i$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$b=6+2\sqrt{6}i b=-2\sqrt{6}i+6$$