(6-x)2x=18 eching

$$(6-x)2x=18$$

x uchun yechish

$$x=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\left(12-2x\right)x=18$$

12-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x-2x^{2}=18$$

Ikkala tarafdan 18 ni ayirish.

$$12x-2x^{2}-18=0$$

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.

$$-2x^{2}+12x-18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 12 ni b va -18 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+8\left(-18\right)}}{2\left(-2\right)}$$

8 ni -18 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-144}}{2\left(-2\right)}$$

144 ni -144 ga qo'shish.

$$x=\frac{-12±\sqrt{0}}{2\left(-2\right)}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{12}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

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

-12 ni -4 ga bo'lish.

$$x=3$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$\left(12-2x\right)x=18$$

12-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$12x-2x^{2}=18$$

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

$$-2x^{2}+12x=18$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+12x}{-2}=\frac{18}{-2}$$

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

$$x^{2}+\frac{12}{-2}x=\frac{18}{-2}$$

12 ni -2 ga bo'lish.

$$x^{2}-6x=\frac{18}{-2}$$

18 ni -2 ga bo'lish.

$$x^{2}-6x=-9$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=-9+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-9+9$$

-9 ni 9 ga qo'shish.

$$x^{2}-6x+9=0$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-3=0 x-3=0$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=3 x=3$$

Tenglama yechildi. Yechimlar bir xil.

$$x=3$$