(32-2x)x=120 eching

$$(32-2x)x=120$$

x uchun yechish

$$x=6$$

$$x=10$$

Kvadrat tenglamalaridan foydalanish qoidalari

32-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$32x-2x^{2}=120$$

Ikkala tarafdan 120 ni ayirish.

$$32x-2x^{2}-120=0$$

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.

$$-2x^{2}+32x-120=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 32 ni b va -120 ni c bilan almashtiring.

$$x=\frac{-32±\sqrt{32^{2}-4\left(-2\right)\left(-120\right)}}{2\left(-2\right)}$$

32 kvadratini chiqarish.

$$x=\frac{-32±\sqrt{1024-4\left(-2\right)\left(-120\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024+8\left(-120\right)}}{2\left(-2\right)}$$

8 ni -120 marotabaga ko'paytirish.

$$x=\frac{-32±\sqrt{1024-960}}{2\left(-2\right)}$$

1024 ni -960 ga qo'shish.

$$x=\frac{-32±\sqrt{64}}{2\left(-2\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-32±8}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-32±8}{-4}$$

x=\frac{-32±8}{-4} tenglamasini yeching, bunda ± musbat. -32 ni 8 ga qo'shish.

$$x=-\frac{24}{-4}$$

-24 ni -4 ga bo'lish.

$$x=6$$

x=\frac{-32±8}{-4} tenglamasini yeching, bunda ± manfiy. -32 dan 8 ni ayirish.

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

-40 ni -4 ga bo'lish.

$$x=10$$

Tenglama yechildi.

$$x=6 x=10$$

Kvadratni yakunlash bo'yicha qadamlar

32-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$32x-2x^{2}=120$$

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

$$-2x^{2}+32x=120$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+32x}{-2}=\frac{120}{-2}$$

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

$$x^{2}+\frac{32}{-2}x=\frac{120}{-2}$$

32 ni -2 ga bo'lish.

$$x^{2}-16x=\frac{120}{-2}$$

120 ni -2 ga bo'lish.

$$x^{2}-16x=-60$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-16x+\left(-8\right)^{2}=-60+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=-60+64$$

-60 ni 64 ga qo'shish.

$$x^{2}-16x+64=4$$

x^{2}-16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-8\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-8=2 x-8=-2$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10 x=6$$