-x^2-2x+3=3 eching

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

x uchun yechish

$$x=-2$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

O‘zidan 3 ayirilsa 0 qoladi.

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

3 dan 3 ni ayirish.

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

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 0 ni c bilan almashtiring.

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

\left(-2\right)^{2} ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±2}{-2}$$

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

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

4 ni -2 ga bo'lish.

$$x=-2$$

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

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-2 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

O‘zidan 3 ayirilsa 0 qoladi.

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

3 dan 3 ni ayirish.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-2x}{-1}=\frac{0}{-1}$$

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

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

-2 ni -1 ga bo'lish.

$$x^{2}+2x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

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

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.

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

1 kvadratini chiqarish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=0 x=-2$$