385=(2x+2)*(2x+3) eching

$$385=(2x+2) \times (2x+3)$$

x uchun yechish

$$x = \frac{\sqrt{1541} - 5}{4} \approx 8,563893213$$

$$x=\frac{-\sqrt{1541}-5}{4}\approx -11,063893213$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x+2 ga 2x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$385=4x^{2}+10x+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$4x^{2}+10x+6=385$$

Ikkala tarafdan 385 ni ayirish.

$$4x^{2}+10x+6-385=0$$

-379 olish uchun 6 dan 385 ni ayirish.

$$4x^{2}+10x-379=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 10 ni b va -379 ni c bilan almashtiring.

$$x=\frac{-10±\sqrt{10^{2}-4\times 4\left(-379\right)}}{2\times 4}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4\times 4\left(-379\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100-16\left(-379\right)}}{2\times 4}$$

-16 ni -379 marotabaga ko'paytirish.

$$x=\frac{-10±\sqrt{100+6064}}{2\times 4}$$

100 ni 6064 ga qo'shish.

$$x=\frac{-10±\sqrt{6164}}{2\times 4}$$

6164 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±2\sqrt{1541}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-10±2\sqrt{1541}}{8}$$

x=\frac{-10±2\sqrt{1541}}{8} tenglamasini yeching, bunda ± musbat. -10 ni 2\sqrt{1541} ga qo'shish.

$$x=\frac{2\sqrt{1541}-10}{8}$$

-10+2\sqrt{1541} ni 8 ga bo'lish.

$$x=\frac{\sqrt{1541}-5}{4}$$

x=\frac{-10±2\sqrt{1541}}{8} tenglamasini yeching, bunda ± manfiy. -10 dan 2\sqrt{1541} ni ayirish.

$$x=\frac{-2\sqrt{1541}-10}{8}$$

-10-2\sqrt{1541} ni 8 ga bo'lish.

$$x=\frac{-\sqrt{1541}-5}{4}$$

Tenglama yechildi.

$$x=\frac{\sqrt{1541}-5}{4} x=\frac{-\sqrt{1541}-5}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

2x+2 ga 2x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$385=4x^{2}+10x+6$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$4x^{2}+10x+6=385$$

Ikkala tarafdan 6 ni ayirish.

$$4x^{2}+10x=385-6$$

379 olish uchun 385 dan 6 ni ayirish.

$$4x^{2}+10x=379$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}+10x}{4}=\frac{379}{4}$$

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

$$x^{2}+\frac{10}{4}x=\frac{379}{4}$$

\frac{10}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{5}{2}x=\frac{379}{4}$$

\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.

$$x^{2}+\frac{5}{2}x+\left(\frac{5}{4}\right)^{2}=\frac{379}{4}+\left(\frac{5}{4}\right)^{2}$$

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

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{379}{4}+\frac{25}{16}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{379}{4} ni \frac{25}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{5}{2}x+\frac{25}{16}=\frac{1541}{16}$$

x^{2}+\frac{5}{2}x+\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.

$$\left(x+\frac{5}{4}\right)^{2}=\frac{1541}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{5}{4}\right)^{2}}=\sqrt{\frac{1541}{16}}$$

Qisqartirish.

$$x+\frac{5}{4}=\frac{\sqrt{1541}}{4} x+\frac{5}{4}=-\frac{\sqrt{1541}}{4}$$

Tenglamaning ikkala tarafidan \frac{5}{4} ni ayirish.

$$x=\frac{\sqrt{1541}-5}{4} x=\frac{-\sqrt{1541}-5}{4}$$