3x(-8+x)=x^2+8 eching

$$3 x ( - 8 + x ) = x ^ { 2 } + 8$$

x uchun yechish

$$x=2\sqrt{10}+6\approx 12,32455532$$

$$x=6-2\sqrt{10}\approx -0,32455532$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga -8+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-24x+3x^{2}=x^{2}+8$$

Ikkala tarafdan x^{2} ni ayirish.

$$-24x+3x^{2}-x^{2}=8$$

2x^{2} ni olish uchun 3x^{2} va -x^{2} ni birlashtirish.

$$-24x+2x^{2}=8$$

Ikkala tarafdan 8 ni ayirish.

$$-24x+2x^{2}-8=0$$

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.

$$2x^{2}-24x-8=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -24 ni b va -8 ni c bilan almashtiring.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

-24 kvadratini chiqarish.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 2\left(-8\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-8\left(-8\right)}}{2\times 2}$$

-8 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576+64}}{2\times 2}$$

576 ni 64 ga qo'shish.

$$x=\frac{-\left(-24\right)±\sqrt{640}}{2\times 2}$$

640 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±8\sqrt{10}}{2\times 2}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±8\sqrt{10}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{24±8\sqrt{10}}{4}$$

x=\frac{24±8\sqrt{10}}{4} tenglamasini yeching, bunda ± musbat. 24 ni 8\sqrt{10} ga qo'shish.

$$x=\frac{8\sqrt{10}+24}{4}$$

24+8\sqrt{10} ni 4 ga bo'lish.

$$x=2\sqrt{10}+6$$

x=\frac{24±8\sqrt{10}}{4} tenglamasini yeching, bunda ± manfiy. 24 dan 8\sqrt{10} ni ayirish.

$$x=\frac{24-8\sqrt{10}}{4}$$

24-8\sqrt{10} ni 4 ga bo'lish.

$$x=6-2\sqrt{10}$$

Tenglama yechildi.

$$x=2\sqrt{10}+6 x=6-2\sqrt{10}$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga -8+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-24x+3x^{2}=x^{2}+8$$

Ikkala tarafdan x^{2} ni ayirish.

$$-24x+3x^{2}-x^{2}=8$$

2x^{2} ni olish uchun 3x^{2} va -x^{2} ni birlashtirish.

$$-24x+2x^{2}=8$$

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

$$2x^{2}-24x=8$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-24x}{2}=\frac{8}{2}$$

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

$$x^{2}+\left(-\frac{24}{2}\right)x=\frac{8}{2}$$

-24 ni 2 ga bo'lish.

$$x^{2}-12x=\frac{8}{2}$$

8 ni 2 ga bo'lish.

$$x^{2}-12x=4$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=4+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=4+36$$

4 ni 36 ga qo'shish.

$$x^{2}-12x+36=40$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=40$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{40}$$

Qisqartirish.

$$x-6=2\sqrt{10} x-6=-2\sqrt{10}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{10}+6 x=6-2\sqrt{10}$$