(x-1)(x+2)+3x=4(x-2)-(x-12) eching

$$( x - 1 ) ( x + 2 ) + 3 x = 4 ( x - 2 ) - ( x - 12 )$$

x uchun yechish

$$x=-3$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+x-2+3x=4\left(x-2\right)-\left(x-12\right)$$

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

$$x^{2}+4x-2=4\left(x-2\right)-\left(x-12\right)$$

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

$$x^{2}+4x-2=4x-8-\left(x-12\right)$$

x-12 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}+4x-2=4x-8-x+12$$

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

$$x^{2}+4x-2=3x-8+12$$

4 olish uchun -8 va 12'ni qo'shing.

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

Ikkala tarafdan 3x ni ayirish.

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

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

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

Ikkala tarafdan 4 ni ayirish.

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

-6 olish uchun -2 dan 4 ni ayirish.

$$x^{2}+x-6=0$$

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 -6 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-6\right)}}{2}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-6\right)}}{2}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+24}}{2}$$

1 ni 24 ga qo'shish.

$$x=\frac{-1±\sqrt{25}}{2}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±5}{2}$$

x=\frac{-1±5}{2} tenglamasini yeching, bunda ± musbat. -1 ni 5 ga qo'shish.

$$x=\frac{4}{2}$$

4 ni 2 ga bo'lish.

$$x=2$$

x=\frac{-1±5}{2} tenglamasini yeching, bunda ± manfiy. -1 dan 5 ni ayirish.

$$x=-\frac{6}{2}$$

-6 ni 2 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=2 x=-3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+x-2+3x=4\left(x-2\right)-\left(x-12\right)$$

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

$$x^{2}+4x-2=4\left(x-2\right)-\left(x-12\right)$$

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

$$x^{2}+4x-2=4x-8-\left(x-12\right)$$

x-12 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}+4x-2=4x-8-x+12$$

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

$$x^{2}+4x-2=3x-8+12$$

4 olish uchun -8 va 12'ni qo'shing.

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

Ikkala tarafdan 3x ni ayirish.

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

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

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

2 ni ikki tarafga qo’shing.

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

6 olish uchun 4 va 2'ni qo'shing.

$$x^{2}+x=6$$

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.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=6+\left(\frac{1}{2}\right)^{2}$$

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

$$x^{2}+x+\frac{1}{4}=6+\frac{1}{4}$$

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

$$x^{2}+x+\frac{1}{4}=\frac{25}{4}$$

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.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{5}{2} x+\frac{1}{2}=-\frac{5}{2}$$

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

$$x=2 x=-3$$