(x+2)(x+4)=12 eching

$$( x + 2 ) ( x + 4 ) = 12$$

x uchun yechish (complex solution)

$$x=\sqrt{13}-3\approx 0,605551275$$

$$x=-\left(\sqrt{13}+3\right)\approx -6,605551275$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+6x+8=12$$

Ikkala tarafdan 12 ni ayirish.

$$x^{2}+6x+8-12=0$$

-4 olish uchun 8 dan 12 ni ayirish.

$$x^{2}+6x-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va -4 ni c bilan almashtiring.

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

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\left(-4\right)}}{2}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+16}}{2}$$

36 ni 16 ga qo'shish.

$$x=\frac{-6±\sqrt{52}}{2}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{13}}{2}$$

x=\frac{-6±2\sqrt{13}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}-6}{2}$$

-6+2\sqrt{13} ni 2 ga bo'lish.

$$x=\sqrt{13}-3$$

x=\frac{-6±2\sqrt{13}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{13} ni ayirish.

$$x=\frac{-2\sqrt{13}-6}{2}$$

-6-2\sqrt{13} ni 2 ga bo'lish.

$$x=-\sqrt{13}-3$$

Tenglama yechildi.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+6x+8=12$$

Ikkala tarafdan 8 ni ayirish.

$$x^{2}+6x=12-8$$

4 olish uchun 12 dan 8 ni ayirish.

$$x^{2}+6x=4$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+6x+3^{2}=4+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=4+9$$

4 ni 9 ga qo'shish.

$$x^{2}+6x+9=13$$

x^{2}+6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+3\right)^{2}=13$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{13}$$

Qisqartirish.

$$x+3=\sqrt{13} x+3=-\sqrt{13}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

x uchun yechish

$$x=\sqrt{13}-3\approx 0,605551275$$

$$x=-\sqrt{13}-3\approx -6,605551275$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+6x+8=12$$

Ikkala tarafdan 12 ni ayirish.

$$x^{2}+6x+8-12=0$$

-4 olish uchun 8 dan 12 ni ayirish.

$$x^{2}+6x-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va -4 ni c bilan almashtiring.

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

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\left(-4\right)}}{2}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+16}}{2}$$

36 ni 16 ga qo'shish.

$$x=\frac{-6±\sqrt{52}}{2}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{13}}{2}$$

x=\frac{-6±2\sqrt{13}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}-6}{2}$$

-6+2\sqrt{13} ni 2 ga bo'lish.

$$x=\sqrt{13}-3$$

x=\frac{-6±2\sqrt{13}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{13} ni ayirish.

$$x=\frac{-2\sqrt{13}-6}{2}$$

-6-2\sqrt{13} ni 2 ga bo'lish.

$$x=-\sqrt{13}-3$$

Tenglama yechildi.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+6x+8=12$$

Ikkala tarafdan 8 ni ayirish.

$$x^{2}+6x=12-8$$

4 olish uchun 12 dan 8 ni ayirish.

$$x^{2}+6x=4$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+6x+3^{2}=4+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=4+9$$

4 ni 9 ga qo'shish.

$$x^{2}+6x+9=13$$

x^{2}+6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+3\right)^{2}=13$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{13}$$

Qisqartirish.

$$x+3=\sqrt{13} x+3=-\sqrt{13}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{13}-3 x=-\sqrt{13}-3$$