(x-2)(x+4)=7 eching

$$( x - 2 ) ( x + 4 ) = 7$$

x uchun yechish

$$x=-5$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-2 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+2x-8=7$$

Ikkala tarafdan 7 ni ayirish.

$$x^{2}+2x-8-7=0$$

-15 olish uchun -8 dan 7 ni ayirish.

$$x^{2}+2x-15=0$$

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 -15 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-15\right)}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+60}}{2}$$

4 ni 60 ga qo'shish.

$$x=\frac{-2±\sqrt{64}}{2}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±8}{2}$$

x=\frac{-2±8}{2} tenglamasini yeching, bunda ± musbat. -2 ni 8 ga qo'shish.

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

6 ni 2 ga bo'lish.

$$x=3$$

x=\frac{-2±8}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 8 ni ayirish.

$$x=-\frac{10}{2}$$

-10 ni 2 ga bo'lish.

$$x=-5$$

Tenglama yechildi.

$$x=3 x=-5$$

Kvadratni yakunlash bo'yicha qadamlar

x-2 ga x+4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+2x-8=7$$

8 ni ikki tarafga qo’shing.

$$x^{2}+2x=7+8$$

15 olish uchun 7 va 8'ni qo'shing.

$$x^{2}+2x=15$$

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.

$$x^{2}+2x+1^{2}=15+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=15+1$$

15 ni 1 ga qo'shish.

$$x^{2}+2x+1=16$$

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.

$$\left(x+1\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x+1=4 x+1=-4$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=3 x=-5$$