(14-x)(6x-24)/10=126 eching

$$\frac{ (14-x)(6x-24) }{ 10 } =126$$

x uchun yechish (complex solution)

$$x=9+\sqrt{185}i\approx 9+13,601470509i$$

$$x=-\sqrt{185}i+9\approx 9-13,601470509i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafini 10 ga ko‘paytiring.

$$\left(14-x\right)\left(6x-24\right)=126\times 10$$

14-x ga 6x-24 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$108x-336-6x^{2}=126\times 10$$

1260 hosil qilish uchun 126 va 10 ni ko'paytirish.

$$108x-336-6x^{2}=1260$$

Ikkala tarafdan 1260 ni ayirish.

$$108x-336-6x^{2}-1260=0$$

-1596 olish uchun -336 dan 1260 ni ayirish.

$$108x-1596-6x^{2}=0$$

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.

$$-6x^{2}+108x-1596=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 108 ni b va -1596 ni c bilan almashtiring.

$$x=\frac{-108±\sqrt{108^{2}-4\left(-6\right)\left(-1596\right)}}{2\left(-6\right)}$$

108 kvadratini chiqarish.

$$x=\frac{-108±\sqrt{11664-4\left(-6\right)\left(-1596\right)}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-108±\sqrt{11664+24\left(-1596\right)}}{2\left(-6\right)}$$

24 ni -1596 marotabaga ko'paytirish.

$$x=\frac{-108±\sqrt{11664-38304}}{2\left(-6\right)}$$

11664 ni -38304 ga qo'shish.

$$x=\frac{-108±\sqrt{-26640}}{2\left(-6\right)}$$

-26640 ning kvadrat ildizini chiqarish.

$$x=\frac{-108±12\sqrt{185}i}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-108±12\sqrt{185}i}{-12}$$

x=\frac{-108±12\sqrt{185}i}{-12} tenglamasini yeching, bunda ± musbat. -108 ni 12i\sqrt{185} ga qo'shish.

$$x=\frac{-108+12\sqrt{185}i}{-12}$$

-108+12i\sqrt{185} ni -12 ga bo'lish.

$$x=-\sqrt{185}i+9$$

x=\frac{-108±12\sqrt{185}i}{-12} tenglamasini yeching, bunda ± manfiy. -108 dan 12i\sqrt{185} ni ayirish.

$$x=\frac{-12\sqrt{185}i-108}{-12}$$

-108-12i\sqrt{185} ni -12 ga bo'lish.

$$x=9+\sqrt{185}i$$

Tenglama yechildi.

$$x=-\sqrt{185}i+9 x=9+\sqrt{185}i$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafini 10 ga ko‘paytiring.

$$\left(14-x\right)\left(6x-24\right)=126\times 10$$

14-x ga 6x-24 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$108x-336-6x^{2}=126\times 10$$

1260 hosil qilish uchun 126 va 10 ni ko'paytirish.

$$108x-336-6x^{2}=1260$$

336 ni ikki tarafga qo’shing.

$$108x-6x^{2}=1260+336$$

1596 olish uchun 1260 va 336'ni qo'shing.

$$108x-6x^{2}=1596$$

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

$$-6x^{2}+108x=1596$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6x^{2}+108x}{-6}=\frac{1596}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{108}{-6}x=\frac{1596}{-6}$$

108 ni -6 ga bo'lish.

$$x^{2}-18x=\frac{1596}{-6}$$

1596 ni -6 ga bo'lish.

$$x^{2}-18x=-266$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-18x+\left(-9\right)^{2}=-266+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=-266+81$$

-266 ni 81 ga qo'shish.

$$x^{2}-18x+81=-185$$

x^{2}-18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-9\right)^{2}=-185$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{-185}$$

Qisqartirish.

$$x-9=\sqrt{185}i x-9=-\sqrt{185}i$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=9+\sqrt{185}i x=-\sqrt{185}i+9$$