-2x+12=-80/x eching

$$- 2 x + 12 = - \frac { 80 } { x }$$

x uchun yechish

$$x=-4$$

$$x=10$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$-2xx+x\times 12=-80$$

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

$$-2x^{2}+x\times 12=-80$$

80 ni ikki tarafga qo’shing.

$$-2x^{2}+x\times 12+80=0$$

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.

$$-2x^{2}+12x+80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 12 ni b va 80 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-2\right)\times 80}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+8\times 80}}{2\left(-2\right)}$$

8 ni 80 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+640}}{2\left(-2\right)}$$

144 ni 640 ga qo'shish.

$$x=\frac{-12±\sqrt{784}}{2\left(-2\right)}$$

784 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±28}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±28}{-4}$$

x=\frac{-12±28}{-4} tenglamasini yeching, bunda ± musbat. -12 ni 28 ga qo'shish.

$$x=\frac{16}{-4}$$

16 ni -4 ga bo'lish.

$$x=-4$$

x=\frac{-12±28}{-4} tenglamasini yeching, bunda ± manfiy. -12 dan 28 ni ayirish.

$$x=-\frac{40}{-4}$$

-40 ni -4 ga bo'lish.

$$x=10$$

Tenglama yechildi.

$$x=-4 x=10$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$-2xx+x\times 12=-80$$

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

$$-2x^{2}+x\times 12=-80$$

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

$$-2x^{2}+12x=-80$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+12x}{-2}=-\frac{80}{-2}$$

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

$$x^{2}+\frac{12}{-2}x=-\frac{80}{-2}$$

12 ni -2 ga bo'lish.

$$x^{2}-6x=-\frac{80}{-2}$$

-80 ni -2 ga bo'lish.

$$x^{2}-6x=40$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=40+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=40+9$$

40 ni 9 ga qo'shish.

$$x^{2}-6x+9=49$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=49$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{49}$$

Qisqartirish.

$$x-3=7 x-3=-7$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10 x=-4$$