(11x+4)(11x+40)=1612 eching

$$(11x+4)(11x+40)=1612$$

x uchun yechish

$$x=-6$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

11x+4 ga 11x+40 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$121x^{2}+484x+160=1612$$

Ikkala tarafdan 1612 ni ayirish.

$$121x^{2}+484x+160-1612=0$$

-1452 olish uchun 160 dan 1612 ni ayirish.

$$121x^{2}+484x-1452=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 121 ni a, 484 ni b va -1452 ni c bilan almashtiring.

$$x=\frac{-484±\sqrt{484^{2}-4\times 121\left(-1452\right)}}{2\times 121}$$

484 kvadratini chiqarish.

$$x=\frac{-484±\sqrt{234256-4\times 121\left(-1452\right)}}{2\times 121}$$

-4 ni 121 marotabaga ko'paytirish.

$$x=\frac{-484±\sqrt{234256-484\left(-1452\right)}}{2\times 121}$$

-484 ni -1452 marotabaga ko'paytirish.

$$x=\frac{-484±\sqrt{234256+702768}}{2\times 121}$$

234256 ni 702768 ga qo'shish.

$$x=\frac{-484±\sqrt{937024}}{2\times 121}$$

937024 ning kvadrat ildizini chiqarish.

$$x=\frac{-484±968}{2\times 121}$$

2 ni 121 marotabaga ko'paytirish.

$$x=\frac{-484±968}{242}$$

x=\frac{-484±968}{242} tenglamasini yeching, bunda ± musbat. -484 ni 968 ga qo'shish.

$$x=\frac{484}{242}$$

484 ni 242 ga bo'lish.

$$x=2$$

x=\frac{-484±968}{242} tenglamasini yeching, bunda ± manfiy. -484 dan 968 ni ayirish.

$$x=-\frac{1452}{242}$$

-1452 ni 242 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=2 x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

11x+4 ga 11x+40 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$121x^{2}+484x+160=1612$$

Ikkala tarafdan 160 ni ayirish.

$$121x^{2}+484x=1612-160$$

1452 olish uchun 1612 dan 160 ni ayirish.

$$121x^{2}+484x=1452$$

Ikki tarafini 121 ga bo‘ling.

$$\frac{121x^{2}+484x}{121}=\frac{1452}{121}$$

121 ga bo'lish 121 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{484}{121}x=\frac{1452}{121}$$

484 ni 121 ga bo'lish.

$$x^{2}+4x=\frac{1452}{121}$$

1452 ni 121 ga bo'lish.

$$x^{2}+4x=12$$

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

$$x^{2}+4x+2^{2}=12+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=12+4$$

12 ni 4 ga qo'shish.

$$x^{2}+4x+4=16$$

x^{2}+4x+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.

$$\left(x+2\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x+2=4 x+2=-4$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=2 x=-6$$