x*(x+1)=2256 eching

$$x \times (x+1)=2256$$

x uchun yechish

$$x=-48$$

$$x=47$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x=2256$$

Ikkala tarafdan 2256 ni ayirish.

$$x^{2}+x-2256=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 1 ni b va -2256 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-2256\right)}}{2}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-2256\right)}}{2}$$

-4 ni -2256 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+9024}}{2}$$

1 ni 9024 ga qo'shish.

$$x=\frac{-1±\sqrt{9025}}{2}$$

9025 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±95}{2}$$

x=\frac{-1±95}{2} tenglamasini yeching, bunda ± musbat. -1 ni 95 ga qo'shish.

$$x=\frac{94}{2}$$

94 ni 2 ga bo'lish.

$$x=47$$

x=\frac{-1±95}{2} tenglamasini yeching, bunda ± manfiy. -1 dan 95 ni ayirish.

$$x=-\frac{96}{2}$$

-96 ni 2 ga bo'lish.

$$x=-48$$

Tenglama yechildi.

$$x=47 x=-48$$

Kvadratni yakunlash bo'yicha qadamlar

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+x=2256$$

1 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{2} olish uchun. Keyin, \frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=2256+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=2256+\frac{1}{4}$$

2256 ni \frac{1}{4} ga qo'shish.

$$x^{2}+x+\frac{1}{4}=\frac{9025}{4}$$

x^{2}+x+\frac{1}{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.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{9025}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9025}{4}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{95}{2} x+\frac{1}{2}=-\frac{95}{2}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=47 x=-48$$