(5-2w)w=52 eching

$$( 5 - 2 w ) w = 52$$

w uchun yechish

$$w=\frac{-\sqrt{391}i+5}{4}\approx 1,25-4,943429983i$$

$$w=\frac{5+\sqrt{391}i}{4}\approx 1,25+4,943429983i$$

Kvadrat tenglamalaridan foydalanish qoidalari

5-2w ga w ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5w-2w^{2}=52$$

Ikkala tarafdan 52 ni ayirish.

$$5w-2w^{2}-52=0$$

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.

$$-2w^{2}+5w-52=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 5 ni b va -52 ni c bilan almashtiring.

$$w=\frac{-5±\sqrt{5^{2}-4\left(-2\right)\left(-52\right)}}{2\left(-2\right)}$$

5 kvadratini chiqarish.

$$w=\frac{-5±\sqrt{25-4\left(-2\right)\left(-52\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$w=\frac{-5±\sqrt{25+8\left(-52\right)}}{2\left(-2\right)}$$

8 ni -52 marotabaga ko'paytirish.

$$w=\frac{-5±\sqrt{25-416}}{2\left(-2\right)}$$

25 ni -416 ga qo'shish.

$$w=\frac{-5±\sqrt{-391}}{2\left(-2\right)}$$

-391 ning kvadrat ildizini chiqarish.

$$w=\frac{-5±\sqrt{391}i}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$w=\frac{-5±\sqrt{391}i}{-4}$$

w=\frac{-5±\sqrt{391}i}{-4} tenglamasini yeching, bunda ± musbat. -5 ni i\sqrt{391} ga qo'shish.

$$w=\frac{-5+\sqrt{391}i}{-4}$$

-5+i\sqrt{391} ni -4 ga bo'lish.

$$w=\frac{-\sqrt{391}i+5}{4}$$

w=\frac{-5±\sqrt{391}i}{-4} tenglamasini yeching, bunda ± manfiy. -5 dan i\sqrt{391} ni ayirish.

$$w=\frac{-\sqrt{391}i-5}{-4}$$

-5-i\sqrt{391} ni -4 ga bo'lish.

$$w=\frac{5+\sqrt{391}i}{4}$$

Tenglama yechildi.

$$w=\frac{-\sqrt{391}i+5}{4} w=\frac{5+\sqrt{391}i}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

5-2w ga w ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5w-2w^{2}=52$$

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

$$-2w^{2}+5w=52$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2w^{2}+5w}{-2}=\frac{52}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$w^{2}+\frac{5}{-2}w=\frac{52}{-2}$$

5 ni -2 ga bo'lish.

$$w^{2}-\frac{5}{2}w=\frac{52}{-2}$$

52 ni -2 ga bo'lish.

$$w^{2}-\frac{5}{2}w=-26$$

-\frac{5}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{4} olish uchun. Keyin, -\frac{5}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$w^{2}-\frac{5}{2}w+\left(-\frac{5}{4}\right)^{2}=-26+\left(-\frac{5}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{4} kvadratini chiqarish.

$$w^{2}-\frac{5}{2}w+\frac{25}{16}=-26+\frac{25}{16}$$

-26 ni \frac{25}{16} ga qo'shish.

$$w^{2}-\frac{5}{2}w+\frac{25}{16}=-\frac{391}{16}$$

w^{2}-\frac{5}{2}w+\frac{25}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w-\frac{5}{4}\right)^{2}=-\frac{391}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w-\frac{5}{4}\right)^{2}}=\sqrt{-\frac{391}{16}}$$

Qisqartirish.

$$w-\frac{5}{4}=\frac{\sqrt{391}i}{4} w-\frac{5}{4}=-\frac{\sqrt{391}i}{4}$$

\frac{5}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$w=\frac{5+\sqrt{391}i}{4} w=\frac{-\sqrt{391}i+5}{4}$$