3+2x-x^2=x^2-4x+3 eching

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

x uchun yechish

$$x=3$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan x^{2} ni ayirish.

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

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

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

4x ni ikki tarafga qo’shing.

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

6x ni olish uchun 2x va 4x ni birlashtirish.

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

Ikkala tarafdan 3 ni ayirish.

$$3+6x-2x^{2}-3=0$$

0 olish uchun 3 dan 3 ni ayirish.

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

x omili.

$$x\left(6-2x\right)=0$$

Tenglamani yechish uchun x=0 va 6-2x=0 ni yeching.

$$x=0 x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

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

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

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

4x ni ikki tarafga qo’shing.

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

6x ni olish uchun 2x va 4x ni birlashtirish.

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

Ikkala tarafdan 3 ni ayirish.

$$3+6x-2x^{2}-3=0$$

0 olish uchun 3 dan 3 ni ayirish.

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

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.

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

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

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

6^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-6±6}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-6±6}{-4}$$

x=\frac{-6±6}{-4} tenglamasini yeching, bunda ± musbat. -6 ni 6 ga qo'shish.

$$x=\frac{0}{-4}$$

0 ni -4 ga bo'lish.

$$x=0$$

x=\frac{-6±6}{-4} tenglamasini yeching, bunda ± manfiy. -6 dan 6 ni ayirish.

$$x=-\frac{12}{-4}$$

-12 ni -4 ga bo'lish.

$$x=3$$

Tenglama yechildi.

$$x=0 x=3$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

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

-2x^{2} ni olish uchun -x^{2} va -x^{2} ni birlashtirish.

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

4x ni ikki tarafga qo’shing.

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

6x ni olish uchun 2x va 4x ni birlashtirish.

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

Ikkala tarafdan 3 ni ayirish.

$$6x-2x^{2}=3-3$$

0 olish uchun 3 dan 3 ni ayirish.

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

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

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

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+6x}{-2}=\frac{0}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{6}{-2}x=\frac{0}{-2}$$

6 ni -2 ga bo'lish.

$$x^{2}-3x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

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

-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.

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

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

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=3 x=0$$