9-3x/9=15-9x/9x eching

$$\frac{ 9-3x }{ 9 } = \frac{ 15-9x }{ 9x }$$

x uchun yechish

$$x=1$$

$$x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 9x ga, 9,9x ning eng kichik karralisiga ko‘paytiring.

$$x\left(9-3x\right)=15-9x$$

x ga 9-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3x^{2}=15-9x$$

Ikkala tarafdan 15 ni ayirish.

$$9x-3x^{2}-15=-9x$$

9x ni ikki tarafga qo’shing.

$$9x-3x^{2}-15+9x=0$$

18x ni olish uchun 9x va 9x ni birlashtirish.

$$18x-3x^{2}-15=0$$

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.

$$-3x^{2}+18x-15=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, 18 ni b va -15 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-3\right)\left(-15\right)}}{2\left(-3\right)}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-3\right)\left(-15\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+12\left(-15\right)}}{2\left(-3\right)}$$

12 ni -15 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-180}}{2\left(-3\right)}$$

324 ni -180 ga qo'shish.

$$x=\frac{-18±\sqrt{144}}{2\left(-3\right)}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±12}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-18±12}{-6}$$

x=\frac{-18±12}{-6} tenglamasini yeching, bunda ± musbat. -18 ni 12 ga qo'shish.

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

-6 ni -6 ga bo'lish.

$$x=1$$

x=\frac{-18±12}{-6} tenglamasini yeching, bunda ± manfiy. -18 dan 12 ni ayirish.

$$x=-\frac{30}{-6}$$

-30 ni -6 ga bo'lish.

$$x=5$$

Tenglama yechildi.

$$x=1 x=5$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 9x ga, 9,9x ning eng kichik karralisiga ko‘paytiring.

$$x\left(9-3x\right)=15-9x$$

x ga 9-3x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x-3x^{2}=15-9x$$

9x ni ikki tarafga qo’shing.

$$9x-3x^{2}+9x=15$$

18x ni olish uchun 9x va 9x ni birlashtirish.

$$18x-3x^{2}=15$$

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

$$-3x^{2}+18x=15$$

Ikki tarafini -3 ga bo‘ling.

$$\frac{-3x^{2}+18x}{-3}=\frac{15}{-3}$$

-3 ga bo'lish -3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{18}{-3}x=\frac{15}{-3}$$

18 ni -3 ga bo'lish.

$$x^{2}-6x=\frac{15}{-3}$$

15 ni -3 ga bo'lish.

$$x^{2}-6x=-5$$

-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.

$$x^{2}-6x+\left(-3\right)^{2}=-5+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=-5+9$$

-5 ni 9 ga qo'shish.

$$x^{2}-6x+9=4$$

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-3=2 x-3=-2$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=1$$