4+2x/4=4+7x/4+2x eching

$$\frac{ 4+2x }{ 4 } = \frac{ 4+7x }{ 4+2x }$$

x uchun yechish

$$x=3$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(x+2\right) ga, 4,4+2x ning eng kichik karralisiga ko‘paytiring.

$$\left(x+2\right)\left(4+2x\right)=2\left(4+7x\right)$$

x+2 ga 4+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8x+2x^{2}+8=2\left(4+7x\right)$$

2 ga 4+7x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x+2x^{2}+8=8+14x$$

Ikkala tarafdan 8 ni ayirish.

$$8x+2x^{2}+8-8=14x$$

0 olish uchun 8 dan 8 ni ayirish.

$$8x+2x^{2}=14x$$

Ikkala tarafdan 14x ni ayirish.

$$8x+2x^{2}-14x=0$$

-6x ni olish uchun 8x va -14x ni birlashtirish.

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

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.

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

\left(-6\right)^{2} ning kvadrat ildizini chiqarish.

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

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6}{2\times 2}$$

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.

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

12 ni 4 ga bo'lish.

$$x=3$$

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

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

0 ni 4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=3 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -2 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 4\left(x+2\right) ga, 4,4+2x ning eng kichik karralisiga ko‘paytiring.

$$\left(x+2\right)\left(4+2x\right)=2\left(4+7x\right)$$

x+2 ga 4+2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8x+2x^{2}+8=2\left(4+7x\right)$$

2 ga 4+7x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x+2x^{2}+8=8+14x$$

Ikkala tarafdan 14x ni ayirish.

$$8x+2x^{2}+8-14x=8$$

-6x ni olish uchun 8x va -14x ni birlashtirish.

$$-6x+2x^{2}+8=8$$

Ikkala tarafdan 8 ni ayirish.

$$-6x+2x^{2}=8-8$$

0 olish uchun 8 dan 8 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.

$$x^{2}+\left(-\frac{6}{2}\right)x=\frac{0}{2}$$

-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.

$$x=3 x=0$$