5d^2+9d+5=3d^2 eching

$$5 d ^ { 2 } + 9 d + 5 = 3 d ^ { 2 }$$

d uchun yechish

$$d=\frac{\sqrt{41}-9}{4}\approx -0,649218941$$

$$d=\frac{-\sqrt{41}-9}{4}\approx -3,850781059$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3d^{2} ni ayirish.

$$5d^{2}+9d+5-3d^{2}=0$$

2d^{2} ni olish uchun 5d^{2} va -3d^{2} ni birlashtirish.

$$2d^{2}+9d+5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 9 ni b va 5 ni c bilan almashtiring.

$$d=\frac{-9±\sqrt{9^{2}-4\times 2\times 5}}{2\times 2}$$

9 kvadratini chiqarish.

$$d=\frac{-9±\sqrt{81-4\times 2\times 5}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$d=\frac{-9±\sqrt{81-8\times 5}}{2\times 2}$$

-8 ni 5 marotabaga ko'paytirish.

$$d=\frac{-9±\sqrt{81-40}}{2\times 2}$$

81 ni -40 ga qo'shish.

$$d=\frac{-9±\sqrt{41}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$d=\frac{-9±\sqrt{41}}{4}$$

d=\frac{-9±\sqrt{41}}{4} tenglamasini yeching, bunda ± musbat. -9 ni \sqrt{41} ga qo'shish.

$$d=\frac{\sqrt{41}-9}{4}$$

d=\frac{-9±\sqrt{41}}{4} tenglamasini yeching, bunda ± manfiy. -9 dan \sqrt{41} ni ayirish.

$$d=\frac{-\sqrt{41}-9}{4}$$

Tenglama yechildi.

$$d=\frac{\sqrt{41}-9}{4} d=\frac{-\sqrt{41}-9}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 3d^{2} ni ayirish.

$$5d^{2}+9d+5-3d^{2}=0$$

2d^{2} ni olish uchun 5d^{2} va -3d^{2} ni birlashtirish.

$$2d^{2}+9d+5=0$$

Ikkala tarafdan 5 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2d^{2}+9d=-5$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2d^{2}+9d}{2}=-\frac{5}{2}$$

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

$$d^{2}+\frac{9}{2}d=-\frac{5}{2}$$

\frac{9}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{4} olish uchun. Keyin, \frac{9}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$d^{2}+\frac{9}{2}d+\left(\frac{9}{4}\right)^{2}=-\frac{5}{2}+\left(\frac{9}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{4} kvadratini chiqarish.

$$d^{2}+\frac{9}{2}d+\frac{81}{16}=-\frac{5}{2}+\frac{81}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{5}{2} ni \frac{81}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$d^{2}+\frac{9}{2}d+\frac{81}{16}=\frac{41}{16}$$

d^{2}+\frac{9}{2}d+\frac{81}{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.

$$\left(d+\frac{9}{4}\right)^{2}=\frac{41}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(d+\frac{9}{4}\right)^{2}}=\sqrt{\frac{41}{16}}$$

Qisqartirish.

$$d+\frac{9}{4}=\frac{\sqrt{41}}{4} d+\frac{9}{4}=-\frac{\sqrt{41}}{4}$$

Tenglamaning ikkala tarafidan \frac{9}{4} ni ayirish.

$$d=\frac{\sqrt{41}-9}{4} d=\frac{-\sqrt{41}-9}{4}$$