x(x-5)+2(x-1)=(x+1) eching

$$x ( x - 5 ) + 2 ( x - 1 ) = ( x + 1 )$$

x uchun yechish

$$x=\sqrt{7}+2\approx 4,645751311$$

$$x=2-\sqrt{7}\approx -0,645751311$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-5x+2\left(x-1\right)=x+1$$

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

$$x^{2}-5x+2x-2=x+1$$

-3x ni olish uchun -5x va 2x ni birlashtirish.

$$x^{2}-3x-2=x+1$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-3x-2-x=1$$

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

$$x^{2}-4x-2=1$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}-4x-2-1=0$$

-3 olish uchun -2 dan 1 ni ayirish.

$$x^{2}-4x-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va -3 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-3\right)}}{2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+12}}{2}$$

16 ni 12 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{28}}{2}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{7}}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{7}}{2}$$

x=\frac{4±2\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{7} ga qo'shish.

$$x=\frac{2\sqrt{7}+4}{2}$$

4+2\sqrt{7} ni 2 ga bo'lish.

$$x=\sqrt{7}+2$$

x=\frac{4±2\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{7} ni ayirish.

$$x=\frac{4-2\sqrt{7}}{2}$$

4-2\sqrt{7} ni 2 ga bo'lish.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

x ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-5x+2\left(x-1\right)=x+1$$

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

$$x^{2}-5x+2x-2=x+1$$

-3x ni olish uchun -5x va 2x ni birlashtirish.

$$x^{2}-3x-2=x+1$$

Ikkala tarafdan x ni ayirish.

$$x^{2}-3x-2-x=1$$

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

$$x^{2}-4x-2=1$$

2 ni ikki tarafga qo’shing.

$$x^{2}-4x=1+2$$

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

$$x^{2}-4x=3$$

-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.

$$x^{2}-4x+\left(-2\right)^{2}=3+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=3+4$$

3 ni 4 ga qo'shish.

$$x^{2}-4x+4=7$$

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.

$$\left(x-2\right)^{2}=7$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{7}$$

Qisqartirish.

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

2 ni tenglamaning ikkala tarafiga qo'shish.

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