2/5left(x+2right)+2/15x=1/30 eching

$$\frac{ 2 }{ 5 \left( x+2 \right) } + \frac{ 2 }{ 15x } = \frac{ 1 }{ 30 }$$

x uchun yechish

$$x=\sqrt{57}+7\approx 14,549834435$$

$$x=7-\sqrt{57}\approx -0,549834435$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati -2,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 30x\left(x+2\right) ga, 5\left(x+2\right),15x,30 ning eng kichik karralisiga ko‘paytiring.

$$6x\times 2+\left(2x+4\right)\times 2=x\left(x+2\right)$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$12x+\left(2x+4\right)\times 2=x\left(x+2\right)$$

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

$$12x+4x+8=x\left(x+2\right)$$

16x ni olish uchun 12x va 4x ni birlashtirish.

$$16x+8=x\left(x+2\right)$$

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

$$16x+8=x^{2}+2x$$

Ikkala tarafdan x^{2} ni ayirish.

$$16x+8-x^{2}=2x$$

Ikkala tarafdan 2x ni ayirish.

$$16x+8-x^{2}-2x=0$$

14x ni olish uchun 16x va -2x ni birlashtirish.

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

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 14 ni b va 8 ni c bilan almashtiring.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

14 kvadratini chiqarish.

$$x=\frac{-14±\sqrt{196-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+4\times 8}}{2\left(-1\right)}$$

4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-14±\sqrt{196+32}}{2\left(-1\right)}$$

196 ni 32 ga qo'shish.

$$x=\frac{-14±\sqrt{228}}{2\left(-1\right)}$$

228 ning kvadrat ildizini chiqarish.

$$x=\frac{-14±2\sqrt{57}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-14±2\sqrt{57}}{-2}$$

x=\frac{-14±2\sqrt{57}}{-2} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{57} ga qo'shish.

$$x=\frac{2\sqrt{57}-14}{-2}$$

-14+2\sqrt{57} ni -2 ga bo'lish.

$$x=7-\sqrt{57}$$

x=\frac{-14±2\sqrt{57}}{-2} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{57} ni ayirish.

$$x=\frac{-2\sqrt{57}-14}{-2}$$

-14-2\sqrt{57} ni -2 ga bo'lish.

$$x=\sqrt{57}+7$$

Tenglama yechildi.

$$x=7-\sqrt{57} x=\sqrt{57}+7$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati -2,0 qiymatlaridan birortasiga teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 30x\left(x+2\right) ga, 5\left(x+2\right),15x,30 ning eng kichik karralisiga ko‘paytiring.

$$6x\times 2+\left(2x+4\right)\times 2=x\left(x+2\right)$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$12x+\left(2x+4\right)\times 2=x\left(x+2\right)$$

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

$$12x+4x+8=x\left(x+2\right)$$

16x ni olish uchun 12x va 4x ni birlashtirish.

$$16x+8=x\left(x+2\right)$$

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

$$16x+8=x^{2}+2x$$

Ikkala tarafdan x^{2} ni ayirish.

$$16x+8-x^{2}=2x$$

Ikkala tarafdan 2x ni ayirish.

$$16x+8-x^{2}-2x=0$$

14x ni olish uchun 16x va -2x ni birlashtirish.

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

Ikkala tarafdan 8 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

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

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+14x}{-1}=-\frac{8}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{14}{-1}x=-\frac{8}{-1}$$

14 ni -1 ga bo'lish.

$$x^{2}-14x=-\frac{8}{-1}$$

-8 ni -1 ga bo'lish.

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

-14 ni bo‘lish, x shartining koeffitsienti, 2 ga -7 olish uchun. Keyin, -7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-14x+\left(-7\right)^{2}=8+\left(-7\right)^{2}$$

-7 kvadratini chiqarish.

$$x^{2}-14x+49=8+49$$

8 ni 49 ga qo'shish.

$$x^{2}-14x+49=57$$

x^{2}-14x+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-7\right)^{2}=57$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{57}$$

Qisqartirish.

$$x-7=\sqrt{57} x-7=-\sqrt{57}$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{57}+7 x=7-\sqrt{57}$$