(5x^2+35x+20)=(2x+4) eching

$$( 5 x ^ { 2 } + 35 x + 20 ) = ( 2 x + 4 )$$

x uchun yechish

$$x=\frac{\sqrt{769}-33}{10}\approx -0,526915075$$

$$x=\frac{-\sqrt{769}-33}{10}\approx -6,073084925$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

$$5x^{2}+35x+20-2x=4$$

33x ni olish uchun 35x va -2x ni birlashtirish.

$$5x^{2}+33x+20=4$$

Ikkala tarafdan 4 ni ayirish.

$$5x^{2}+33x+20-4=0$$

16 olish uchun 20 dan 4 ni ayirish.

$$5x^{2}+33x+16=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 33 ni b va 16 ni c bilan almashtiring.

$$x=\frac{-33±\sqrt{33^{2}-4\times 5\times 16}}{2\times 5}$$

33 kvadratini chiqarish.

$$x=\frac{-33±\sqrt{1089-4\times 5\times 16}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-33±\sqrt{1089-20\times 16}}{2\times 5}$$

-20 ni 16 marotabaga ko'paytirish.

$$x=\frac{-33±\sqrt{1089-320}}{2\times 5}$$

1089 ni -320 ga qo'shish.

$$x=\frac{-33±\sqrt{769}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-33±\sqrt{769}}{10}$$

x=\frac{-33±\sqrt{769}}{10} tenglamasini yeching, bunda ± musbat. -33 ni \sqrt{769} ga qo'shish.

$$x=\frac{\sqrt{769}-33}{10}$$

x=\frac{-33±\sqrt{769}}{10} tenglamasini yeching, bunda ± manfiy. -33 dan \sqrt{769} ni ayirish.

$$x=\frac{-\sqrt{769}-33}{10}$$

Tenglama yechildi.

$$x=\frac{\sqrt{769}-33}{10} x=\frac{-\sqrt{769}-33}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

$$5x^{2}+35x+20-2x=4$$

33x ni olish uchun 35x va -2x ni birlashtirish.

$$5x^{2}+33x+20=4$$

Ikkala tarafdan 20 ni ayirish.

$$5x^{2}+33x=4-20$$

-16 olish uchun 4 dan 20 ni ayirish.

$$5x^{2}+33x=-16$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}+33x}{5}=-\frac{16}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{33}{5}x=-\frac{16}{5}$$

\frac{33}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{33}{10} olish uchun. Keyin, \frac{33}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{33}{5}x+\left(\frac{33}{10}\right)^{2}=-\frac{16}{5}+\left(\frac{33}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{33}{10} kvadratini chiqarish.

$$x^{2}+\frac{33}{5}x+\frac{1089}{100}=-\frac{16}{5}+\frac{1089}{100}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{16}{5} ni \frac{1089}{100} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{33}{5}x+\frac{1089}{100}=\frac{769}{100}$$

x^{2}+\frac{33}{5}x+\frac{1089}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{33}{10}\right)^{2}=\frac{769}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{33}{10}\right)^{2}}=\sqrt{\frac{769}{100}}$$

Qisqartirish.

$$x+\frac{33}{10}=\frac{\sqrt{769}}{10} x+\frac{33}{10}=-\frac{\sqrt{769}}{10}$$

Tenglamaning ikkala tarafidan \frac{33}{10} ni ayirish.

$$x=\frac{\sqrt{769}-33}{10} x=\frac{-\sqrt{769}-33}{10}$$