14x+48+24x=x^2+2x eching

$$14 x + 48 + 24 x = x ^ { 2 } + 2 x$$

x uchun yechish

$$x=2\sqrt{93}+18\approx 37,287301522$$

$$x=18-2\sqrt{93}\approx -1,287301522$$

Kvadrat tenglamalaridan foydalanish qoidalari

38x ni olish uchun 14x va 24x ni birlashtirish.

$$38x+48=x^{2}+2x$$

Ikkala tarafdan x^{2} ni ayirish.

$$38x+48-x^{2}=2x$$

Ikkala tarafdan 2x ni ayirish.

$$38x+48-x^{2}-2x=0$$

36x ni olish uchun 38x va -2x ni birlashtirish.

$$36x+48-x^{2}=0$$

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.

$$-x^{2}+36x+48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 36 ni b va 48 ni c bilan almashtiring.

$$x=\frac{-36±\sqrt{36^{2}-4\left(-1\right)\times 48}}{2\left(-1\right)}$$

36 kvadratini chiqarish.

$$x=\frac{-36±\sqrt{1296-4\left(-1\right)\times 48}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-36±\sqrt{1296+4\times 48}}{2\left(-1\right)}$$

4 ni 48 marotabaga ko'paytirish.

$$x=\frac{-36±\sqrt{1296+192}}{2\left(-1\right)}$$

1296 ni 192 ga qo'shish.

$$x=\frac{-36±\sqrt{1488}}{2\left(-1\right)}$$

1488 ning kvadrat ildizini chiqarish.

$$x=\frac{-36±4\sqrt{93}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-36±4\sqrt{93}}{-2}$$

x=\frac{-36±4\sqrt{93}}{-2} tenglamasini yeching, bunda ± musbat. -36 ni 4\sqrt{93} ga qo'shish.

$$x=\frac{4\sqrt{93}-36}{-2}$$

-36+4\sqrt{93} ni -2 ga bo'lish.

$$x=18-2\sqrt{93}$$

x=\frac{-36±4\sqrt{93}}{-2} tenglamasini yeching, bunda ± manfiy. -36 dan 4\sqrt{93} ni ayirish.

$$x=\frac{-4\sqrt{93}-36}{-2}$$

-36-4\sqrt{93} ni -2 ga bo'lish.

$$x=2\sqrt{93}+18$$

Tenglama yechildi.

$$x=18-2\sqrt{93} x=2\sqrt{93}+18$$

Kvadratni yakunlash bo'yicha qadamlar

38x ni olish uchun 14x va 24x ni birlashtirish.

$$38x+48=x^{2}+2x$$

Ikkala tarafdan x^{2} ni ayirish.

$$38x+48-x^{2}=2x$$

Ikkala tarafdan 2x ni ayirish.

$$38x+48-x^{2}-2x=0$$

36x ni olish uchun 38x va -2x ni birlashtirish.

$$36x+48-x^{2}=0$$

Ikkala tarafdan 48 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$36x-x^{2}=-48$$

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

$$-x^{2}+36x=-48$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+36x}{-1}=-\frac{48}{-1}$$

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

$$x^{2}+\frac{36}{-1}x=-\frac{48}{-1}$$

36 ni -1 ga bo'lish.

$$x^{2}-36x=-\frac{48}{-1}$$

-48 ni -1 ga bo'lish.

$$x^{2}-36x=48$$

-36 ni bo‘lish, x shartining koeffitsienti, 2 ga -18 olish uchun. Keyin, -18 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-36x+\left(-18\right)^{2}=48+\left(-18\right)^{2}$$

-18 kvadratini chiqarish.

$$x^{2}-36x+324=48+324$$

48 ni 324 ga qo'shish.

$$x^{2}-36x+324=372$$

x^{2}-36x+324 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-18\right)^{2}=372$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-18\right)^{2}}=\sqrt{372}$$

Qisqartirish.

$$x-18=2\sqrt{93} x-18=-2\sqrt{93}$$

18 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{93}+18 x=18-2\sqrt{93}$$