x(x+4)-(x-2)=20 eching

$$x(x+4)-(x-2)=20$$

x uchun yechish

$$x=-6$$

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+4x-\left(x-2\right)=20$$

x-2 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}+4x-x-\left(-2\right)=20$$

-2 ning teskarisi 2 ga teng.

$$x^{2}+4x-x+2=20$$

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

$$x^{2}+3x+2=20$$

Ikkala tarafdan 20 ni ayirish.

$$x^{2}+3x+2-20=0$$

-18 olish uchun 2 dan 20 ni ayirish.

$$x^{2}+3x-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 3 ni b va -18 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-18\right)}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-18\right)}}{2}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+72}}{2}$$

9 ni 72 ga qo'shish.

$$x=\frac{-3±\sqrt{81}}{2}$$

81 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±9}{2}$$

x=\frac{-3±9}{2} tenglamasini yeching, bunda ± musbat. -3 ni 9 ga qo'shish.

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

6 ni 2 ga bo'lish.

$$x=3$$

x=\frac{-3±9}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 9 ni ayirish.

$$x=-\frac{12}{2}$$

-12 ni 2 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=3 x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+4x-\left(x-2\right)=20$$

x-2 teskarisini topish uchun har birining teskarisini toping.

$$x^{2}+4x-x-\left(-2\right)=20$$

-2 ning teskarisi 2 ga teng.

$$x^{2}+4x-x+2=20$$

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

$$x^{2}+3x+2=20$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}+3x=20-2$$

18 olish uchun 20 dan 2 ni ayirish.

$$x^{2}+3x=18$$

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

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=18+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$x^{2}+3x+\frac{9}{4}=18+\frac{9}{4}$$

18 ni \frac{9}{4} ga qo'shish.

$$x^{2}+3x+\frac{9}{4}=\frac{81}{4}$$

x^{2}+3x+\frac{9}{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.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

$$x+\frac{3}{2}=\frac{9}{2} x+\frac{3}{2}=-\frac{9}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=3 x=-6$$