36=(2x+12)(x+1) eching

$$36=(2x+12)(x+1)$$

x uchun yechish

$$x = \frac{\sqrt{97} - 7}{2} \approx 1,424428901$$

$$x=\frac{-\sqrt{97}-7}{2}\approx -8,424428901$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x+12 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36=2x^{2}+14x+12$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}+14x+12=36$$

Ikkala tarafdan 36 ni ayirish.

$$2x^{2}+14x+12-36=0$$

-24 olish uchun 12 dan 36 ni ayirish.

$$2x^{2}+14x-24=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 14 ni b va -24 ni c bilan almashtiring.

$$x=\frac{-14±\sqrt{14^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\times 2\left(-24\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196-8\left(-24\right)}}{2\times 2}$$

-8 ni -24 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+192}}{2\times 2}$$

196 ni 192 ga qo'shish.

$$x=\frac{-14±\sqrt{388}}{2\times 2}$$

388 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{97}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-14±2\sqrt{97}}{4}$$

x=\frac{-14±2\sqrt{97}}{4} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{97} ga qo'shish.

$$x=\frac{2\sqrt{97}-14}{4}$$

-14+2\sqrt{97} ni 4 ga bo'lish.

$$x=\frac{\sqrt{97}-7}{2}$$

x=\frac{-14±2\sqrt{97}}{4} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{97} ni ayirish.

$$x=\frac{-2\sqrt{97}-14}{4}$$

-14-2\sqrt{97} ni 4 ga bo'lish.

$$x=\frac{-\sqrt{97}-7}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x+12 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$36=2x^{2}+14x+12$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}+14x+12=36$$

Ikkala tarafdan 12 ni ayirish.

$$2x^{2}+14x=36-12$$

24 olish uchun 36 dan 12 ni ayirish.

$$2x^{2}+14x=24$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+14x}{2}=\frac{24}{2}$$

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

$$x^{2}+\frac{14}{2}x=\frac{24}{2}$$

14 ni 2 ga bo'lish.

$$x^{2}+7x=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$x^{2}+7x=12$$

7 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{2} olish uchun. Keyin, \frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=12+\left(\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{2} kvadratini chiqarish.

$$x^{2}+7x+\frac{49}{4}=12+\frac{49}{4}$$

12 ni \frac{49}{4} ga qo'shish.

$$x^{2}+7x+\frac{49}{4}=\frac{97}{4}$$

x^{2}+7x+\frac{49}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{97}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{97}{4}}$$

Qisqartirish.

$$x+\frac{7}{2}=\frac{\sqrt{97}}{2} x+\frac{7}{2}=-\frac{\sqrt{97}}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$