(x+2)(x-6)=3 eching

$$( x + 2 ) ( x - 6 ) = 3$$

x uchun yechish

$$x=\sqrt{19}+2\approx 6,358898944$$

$$x=2-\sqrt{19}\approx -2,358898944$$

Kvadrat tenglamalaridan foydalanish qoidalari

x+2 ga x-6 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

Ikkala tarafdan 3 ni ayirish.

$$x^{2}-4x-12-3=0$$

-15 olish uchun -12 dan 3 ni ayirish.

$$x^{2}-4x-15=0$$

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 -15 ni c bilan almashtiring.

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

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+60}}{2}$$

16 ni 60 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{19}}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{19}}{2}$$

x=\frac{4±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}+4}{2}$$

4+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}+2$$

x=\frac{4±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{19} ni ayirish.

$$x=\frac{4-2\sqrt{19}}{2}$$

4-2\sqrt{19} ni 2 ga bo'lish.

$$x=2-\sqrt{19}$$

Tenglama yechildi.

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$

Kvadratni yakunlash bo'yicha qadamlar

x+2 ga x-6 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

12 ni ikki tarafga qo’shing.

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

15 olish uchun 3 va 12'ni qo'shing.

$$x^{2}-4x=15$$

-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.

$$x^{2}-4x+\left(-2\right)^{2}=15+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=15+4$$

15 ni 4 ga qo'shish.

$$x^{2}-4x+4=19$$

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.

$$\left(x-2\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x-2=\sqrt{19} x-2=-\sqrt{19}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{19}+2 x=2-\sqrt{19}$$