left(2w+18right)left(2w+30right)+576=0 eching

$$\left( 2w+18 \right) \left( 2w+30 \right) +576 = 0$$

w uchun yechish

$$w=-12+3\sqrt{15}i\approx -12+11,618950039i$$

$$w=-3\sqrt{15}i-12\approx -12-11,618950039i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2w+18 ga 2w+30 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4w^{2}+96w+540+576=0$$

1116 olish uchun 540 va 576'ni qo'shing.

$$4w^{2}+96w+1116=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 96 ni b va 1116 ni c bilan almashtiring.

$$w=\frac{-96±\sqrt{96^{2}-4\times 4\times 1116}}{2\times 4}$$

96 kvadratini chiqarish.

$$w=\frac{-96±\sqrt{9216-4\times 4\times 1116}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$w=\frac{-96±\sqrt{9216-16\times 1116}}{2\times 4}$$

-16 ni 1116 marotabaga ko'paytirish.

$$w=\frac{-96±\sqrt{9216-17856}}{2\times 4}$$

9216 ni -17856 ga qo'shish.

$$w=\frac{-96±\sqrt{-8640}}{2\times 4}$$

-8640 ning kvadrat ildizini chiqarish.

$$w=\frac{-96±24\sqrt{15}i}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$w=\frac{-96±24\sqrt{15}i}{8}$$

w=\frac{-96±24\sqrt{15}i}{8} tenglamasini yeching, bunda ± musbat. -96 ni 24i\sqrt{15} ga qo'shish.

$$w=\frac{-96+24\sqrt{15}i}{8}$$

-96+24i\sqrt{15} ni 8 ga bo'lish.

$$w=-12+3\sqrt{15}i$$

w=\frac{-96±24\sqrt{15}i}{8} tenglamasini yeching, bunda ± manfiy. -96 dan 24i\sqrt{15} ni ayirish.

$$w=\frac{-24\sqrt{15}i-96}{8}$$

-96-24i\sqrt{15} ni 8 ga bo'lish.

$$w=-3\sqrt{15}i-12$$

Tenglama yechildi.

$$w=-12+3\sqrt{15}i w=-3\sqrt{15}i-12$$

Kvadratni yakunlash bo'yicha qadamlar

2w+18 ga 2w+30 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4w^{2}+96w+540+576=0$$

1116 olish uchun 540 va 576'ni qo'shing.

$$4w^{2}+96w+1116=0$$

Ikkala tarafdan 1116 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$4w^{2}+96w=-1116$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4w^{2}+96w}{4}=-\frac{1116}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$w^{2}+\frac{96}{4}w=-\frac{1116}{4}$$

96 ni 4 ga bo'lish.

$$w^{2}+24w=-\frac{1116}{4}$$

-1116 ni 4 ga bo'lish.

$$w^{2}+24w=-279$$

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

$$w^{2}+24w+12^{2}=-279+12^{2}$$

12 kvadratini chiqarish.

$$w^{2}+24w+144=-279+144$$

-279 ni 144 ga qo'shish.

$$w^{2}+24w+144=-135$$

w^{2}+24w+144 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w+12\right)^{2}=-135$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w+12\right)^{2}}=\sqrt{-135}$$

Qisqartirish.

$$w+12=3\sqrt{15}i w+12=-3\sqrt{15}i$$

Tenglamaning ikkala tarafidan 12 ni ayirish.

$$w=-12+3\sqrt{15}i w=-3\sqrt{15}i-12$$