78/x+8*7=2x eching

$$7 \frac{ 8 }{ x } +8 \cdot 7 = 2x$$

x uchun yechish

$$x=4\sqrt{14}+14\approx 28,966629547$$

$$x=14-4\sqrt{14}\approx -0,966629547$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$7\times 8+8\times 7x=2xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$7\times 8+8\times 7x=2x^{2}$$

56 hosil qilish uchun 7 va 8 ni ko'paytirish. 56 hosil qilish uchun 8 va 7 ni ko'paytirish.

$$56+56x=2x^{2}$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$56+56x-2x^{2}=0$$

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.

$$-2x^{2}+56x+56=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 56 ni b va 56 ni c bilan almashtiring.

$$x=\frac{-56±\sqrt{56^{2}-4\left(-2\right)\times 56}}{2\left(-2\right)}$$

56 kvadratini chiqarish.

$$x=\frac{-56±\sqrt{3136-4\left(-2\right)\times 56}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-56±\sqrt{3136+8\times 56}}{2\left(-2\right)}$$

8 ni 56 marotabaga ko'paytirish.

$$x=\frac{-56±\sqrt{3136+448}}{2\left(-2\right)}$$

3136 ni 448 ga qo'shish.

$$x=\frac{-56±\sqrt{3584}}{2\left(-2\right)}$$

3584 ning kvadrat ildizini chiqarish.

$$x=\frac{-56±16\sqrt{14}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-56±16\sqrt{14}}{-4}$$

x=\frac{-56±16\sqrt{14}}{-4} tenglamasini yeching, bunda ± musbat. -56 ni 16\sqrt{14} ga qo'shish.

$$x=\frac{16\sqrt{14}-56}{-4}$$

-56+16\sqrt{14} ni -4 ga bo'lish.

$$x=14-4\sqrt{14}$$

x=\frac{-56±16\sqrt{14}}{-4} tenglamasini yeching, bunda ± manfiy. -56 dan 16\sqrt{14} ni ayirish.

$$x=\frac{-16\sqrt{14}-56}{-4}$$

-56-16\sqrt{14} ni -4 ga bo'lish.

$$x=4\sqrt{14}+14$$

Tenglama yechildi.

$$x=14-4\sqrt{14} x=4\sqrt{14}+14$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$7\times 8+8\times 7x=2xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$7\times 8+8\times 7x=2x^{2}$$

56 hosil qilish uchun 7 va 8 ni ko'paytirish. 56 hosil qilish uchun 8 va 7 ni ko'paytirish.

$$56+56x=2x^{2}$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$56+56x-2x^{2}=0$$

Ikkala tarafdan 56 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$56x-2x^{2}=-56$$

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

$$-2x^{2}+56x=-56$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+56x}{-2}=-\frac{56}{-2}$$

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

$$x^{2}+\frac{56}{-2}x=-\frac{56}{-2}$$

56 ni -2 ga bo'lish.

$$x^{2}-28x=-\frac{56}{-2}$$

-56 ni -2 ga bo'lish.

$$x^{2}-28x=28$$

-28 ni bo‘lish, x shartining koeffitsienti, 2 ga -14 olish uchun. Keyin, -14 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-28x+\left(-14\right)^{2}=28+\left(-14\right)^{2}$$

-14 kvadratini chiqarish.

$$x^{2}-28x+196=28+196$$

28 ni 196 ga qo'shish.

$$x^{2}-28x+196=224$$

x^{2}-28x+196 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-14\right)^{2}=224$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{224}$$

Qisqartirish.

$$x-14=4\sqrt{14} x-14=-4\sqrt{14}$$

14 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{14}+14 x=14-4\sqrt{14}$$