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

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

x uchun yechish

$$x=2\sqrt{2}-2\approx 0,828427125$$

$$x=-2\sqrt{2}-2\approx -4,828427125$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

Ikkala tarafdan 2 ni ayirish.

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

-4 olish uchun -2 dan 2 ni ayirish.

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

3x ni ikki tarafga qo’shing.

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

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

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

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 -4 ni c bilan almashtiring.

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

4 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+16}}{2}$$

16 ni 16 ga qo'shish.

$$x=\frac{-4±\sqrt{32}}{2}$$

32 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{2}}{2}$$

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

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

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

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

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

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

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

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

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

3x ni ikki tarafga qo’shing.

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

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

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

2 ni ikki tarafga qo’shing.

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

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

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

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.

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

2 kvadratini chiqarish.

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

4 ni 4 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{8}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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