-x/2*(1-2x)+x=1-x eching

$$- \frac{ x }{ 2 } \times (1-2x)+x=1-x$$

x uchun yechish

$$x=-2$$

$$x=\frac{1}{2}=0,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

2\left(-\frac{x}{2}\right) ni yagona kasrga aylantiring.

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

2 va 2 ni qisqartiring.

$$-x\left(1-2x\right)+2x=2-2x$$

-x ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x ni olish uchun -x va 2x ni birlashtirish.

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

Ikkala tarafdan 2 ni ayirish.

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

2x ni ikki tarafga qo’shing.

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

3x ni olish uchun x va 2x ni birlashtirish.

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

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.

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

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

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

3 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-8\left(-2\right)}}{2\times 2}$$

-8 ni -2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+16}}{2\times 2}$$

9 ni 16 ga qo'shish.

$$x=\frac{-3±\sqrt{25}}{2\times 2}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±5}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±5}{4}$$

x=\frac{-3±5}{4} tenglamasini yeching, bunda ± musbat. -3 ni 5 ga qo'shish.

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

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$

x=\frac{-3±5}{4} tenglamasini yeching, bunda ± manfiy. -3 dan 5 ni ayirish.

$$x=-\frac{8}{4}$$

-8 ni 4 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

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

2\left(-\frac{x}{2}\right) ni yagona kasrga aylantiring.

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

2 va 2 ni qisqartiring.

$$-x\left(1-2x\right)+2x=2-2x$$

-x ga 1-2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x ni olish uchun -x va 2x ni birlashtirish.

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

2x ni ikki tarafga qo’shing.

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

3x ni olish uchun x va 2x ni birlashtirish.

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

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

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

Ikki tarafini 2 ga bo‘ling.

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

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

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

2 ni 2 ga bo'lish.

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

\frac{3}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{4} olish uchun. Keyin, \frac{3}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{2}x+\left(\frac{3}{4}\right)^{2}=1+\left(\frac{3}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{4} kvadratini chiqarish.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=1+\frac{9}{16}$$

1 ni \frac{9}{16} ga qo'shish.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{25}{16}$$

x^{2}+\frac{3}{2}x+\frac{9}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{4}\right)^{2}=\frac{25}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Qisqartirish.

$$x+\frac{3}{4}=\frac{5}{4} x+\frac{3}{4}=-\frac{5}{4}$$

Tenglamaning ikkala tarafidan \frac{3}{4} ni ayirish.

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