-x(x+2)+3=0 eching

$$-x(x+2)+3=0$$

x uchun yechish

$$x=-3$$

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

-x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x\right)x+2\left(-x\right)+3=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-x^{2}+2\left(-1\right)x+3=0$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

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

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 3 ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 3}}{2\left(-1\right)}$$

4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+12}}{2\left(-1\right)}$$

4 ni 12 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{16}}{2\left(-1\right)}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±4}{2\left(-1\right)}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±4}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±4}{-2}$$

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

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

6 ni -2 ga bo'lish.

$$x=-3$$

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

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

-2 ni -2 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=-3 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

-x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(-x\right)x+2\left(-x\right)+3=0$$

Ikkala tarafdan 3 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$\left(-x\right)x+2\left(-x\right)=-3$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$-x^{2}+2\left(-1\right)x=-3$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-2x}{-1}=-\frac{3}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{2}{-1}\right)x=-\frac{3}{-1}$$

-2 ni -1 ga bo'lish.

$$x^{2}+2x=-\frac{3}{-1}$$

-3 ni -1 ga bo'lish.

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

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.

$$x^{2}+2x+1^{2}=3+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=3+1$$

3 ni 1 ga qo'shish.

$$x^{2}+2x+1=4$$

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.

$$\left(x+1\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{4}$$

Qisqartirish.

$$x+1=2 x+1=-2$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=1 x=-3$$