-n(n-3)+1=4n-1 eching

$$- n ( n - 3 ) + 1 = 4 n - 1$$

n uchun yechish

$$n=-2$$

$$n=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

-n ga n-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-n\right)n-3\left(-n\right)+1=4n-1$$

3 hosil qilish uchun -3 va -1 ni ko'paytirish.

$$\left(-n\right)n+3n+1=4n-1$$

Ikkala tarafdan 4n ni ayirish.

$$\left(-n\right)n+3n+1-4n=-1$$

-n ni olish uchun 3n va -4n ni birlashtirish.

$$\left(-n\right)n-n+1=-1$$

1 ni ikki tarafga qo’shing.

$$\left(-n\right)n-n+1+1=0$$

2 olish uchun 1 va 1'ni qo'shing.

$$\left(-n\right)n-n+2=0$$

n^{2} hosil qilish uchun n va n ni ko'paytirish.

$$-n^{2}-n+2=0$$

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 2 ni c bilan almashtiring.

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

-4 ni -1 marotabaga ko'paytirish.

$$n=\frac{-\left(-1\right)±\sqrt{1+4\times 2}}{2\left(-1\right)}$$

4 ni 2 marotabaga ko'paytirish.

$$n=\frac{-\left(-1\right)±\sqrt{1+8}}{2\left(-1\right)}$$

1 ni 8 ga qo'shish.

$$n=\frac{-\left(-1\right)±\sqrt{9}}{2\left(-1\right)}$$

9 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-1\right)±3}{2\left(-1\right)}$$

-1 ning teskarisi 1 ga teng.

$$n=\frac{1±3}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$n=\frac{1±3}{-2}$$

n=\frac{1±3}{-2} tenglamasini yeching, bunda ± musbat. 1 ni 3 ga qo'shish.

$$n=\frac{4}{-2}$$

4 ni -2 ga bo'lish.

$$n=-2$$

n=\frac{1±3}{-2} tenglamasini yeching, bunda ± manfiy. 1 dan 3 ni ayirish.

$$n=-\frac{2}{-2}$$

-2 ni -2 ga bo'lish.

$$n=1$$

Tenglama yechildi.

$$n=-2 n=1$$

Kvadratni yakunlash bo'yicha qadamlar

-n ga n-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-n\right)n-3\left(-n\right)+1=4n-1$$

3 hosil qilish uchun -3 va -1 ni ko'paytirish.

$$\left(-n\right)n+3n+1=4n-1$$

Ikkala tarafdan 4n ni ayirish.

$$\left(-n\right)n+3n+1-4n=-1$$

-n ni olish uchun 3n va -4n ni birlashtirish.

$$\left(-n\right)n-n+1=-1$$

Ikkala tarafdan 1 ni ayirish.

$$\left(-n\right)n-n=-1-1$$

-2 olish uchun -1 dan 1 ni ayirish.

$$\left(-n\right)n-n=-2$$

n^{2} hosil qilish uchun n va n ni ko'paytirish.

$$-n^{2}-n=-2$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-n^{2}-n}{-1}=-\frac{2}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$n^{2}+\left(-\frac{1}{-1}\right)n=-\frac{2}{-1}$$

-1 ni -1 ga bo'lish.

$$n^{2}+n=-\frac{2}{-1}$$

-2 ni -1 ga bo'lish.

$$n^{2}+n=2$$

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.

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

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

$$n^{2}+n+\frac{1}{4}=2+\frac{1}{4}$$

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

$$n^{2}+n+\frac{1}{4}=\frac{9}{4}$$

n^{2}+n+\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.

$$\left(n+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$n+\frac{1}{2}=\frac{3}{2} n+\frac{1}{2}=-\frac{3}{2}$$

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

$$n=1 n=-2$$