(x+3)(x-1)=5 eching

$$( x + 3 ) ( x - 1 ) = 5$$

x uchun yechish

$$x=-4$$

$$x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+3 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+2x-3=5$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}+2x-3-5=0$$

-8 olish uchun -3 dan 5 ni ayirish.

$$x^{2}+2x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-8\right)}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-8\right)}}{2}$$

-4 ni -8 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+32}}{2}$$

4 ni 32 ga qo'shish.

$$x=\frac{-2±\sqrt{36}}{2}$$

36 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±6}{2}$$

x=\frac{-2±6}{2} tenglamasini yeching, bunda ± musbat. -2 ni 6 ga qo'shish.

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

4 ni 2 ga bo'lish.

$$x=2$$

x=\frac{-2±6}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 6 ni ayirish.

$$x=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=2 x=-4$$

Kvadratni yakunlash bo'yicha qadamlar

x+3 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+2x-3=5$$

3 ni ikki tarafga qo’shing.

$$x^{2}+2x=5+3$$

8 olish uchun 5 va 3'ni qo'shing.

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

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

$$x^{2}+2x+1^{2}=8+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=8+1$$

8 ni 1 ga qo'shish.

$$x^{2}+2x+1=9$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x+1=3 x+1=-3$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=2 x=-4$$