96*20=(2-6-2x)(20-x) eching

$$96 \times 20 = ( 2 - 6 - 2 x ) ( 20 - x )$$

x uchun yechish

$$x=\sqrt{1081}+9\approx 41,878564446$$

$$x=9-\sqrt{1081}\approx -23,878564446$$

Kvadrat tenglamalaridan foydalanish qoidalari

1920 hosil qilish uchun 96 va 20 ni ko'paytirish.

$$1920=\left(2-6-2x\right)\left(20-x\right)$$

-4 olish uchun 2 dan 6 ni ayirish.

$$1920=\left(-4-2x\right)\left(20-x\right)$$

-4-2x ga 20-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1920=-80-36x+2x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-80-36x+2x^{2}=1920$$

Ikkala tarafdan 1920 ni ayirish.

$$-80-36x+2x^{2}-1920=0$$

-2000 olish uchun -80 dan 1920 ni ayirish.

$$-2000-36x+2x^{2}=0$$

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.

$$2x^{2}-36x-2000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -36 ni b va -2000 ni c bilan almashtiring.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 2\left(-2000\right)}}{2\times 2}$$

-36 kvadratini chiqarish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 2\left(-2000\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296-8\left(-2000\right)}}{2\times 2}$$

-8 ni -2000 marotabaga ko'paytirish.

$$x=\frac{-\left(-36\right)±\sqrt{1296+16000}}{2\times 2}$$

1296 ni 16000 ga qo'shish.

$$x=\frac{-\left(-36\right)±\sqrt{17296}}{2\times 2}$$

17296 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-36\right)±4\sqrt{1081}}{2\times 2}$$

-36 ning teskarisi 36 ga teng.

$$x=\frac{36±4\sqrt{1081}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{36±4\sqrt{1081}}{4}$$

x=\frac{36±4\sqrt{1081}}{4} tenglamasini yeching, bunda ± musbat. 36 ni 4\sqrt{1081} ga qo'shish.

$$x=\frac{4\sqrt{1081}+36}{4}$$

36+4\sqrt{1081} ni 4 ga bo'lish.

$$x=\sqrt{1081}+9$$

x=\frac{36±4\sqrt{1081}}{4} tenglamasini yeching, bunda ± manfiy. 36 dan 4\sqrt{1081} ni ayirish.

$$x=\frac{36-4\sqrt{1081}}{4}$$

36-4\sqrt{1081} ni 4 ga bo'lish.

$$x=9-\sqrt{1081}$$

Tenglama yechildi.

$$x=\sqrt{1081}+9 x=9-\sqrt{1081}$$

Kvadratni yakunlash bo'yicha qadamlar

1920 hosil qilish uchun 96 va 20 ni ko'paytirish.

$$1920=\left(2-6-2x\right)\left(20-x\right)$$

-4 olish uchun 2 dan 6 ni ayirish.

$$1920=\left(-4-2x\right)\left(20-x\right)$$

-4-2x ga 20-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$1920=-80-36x+2x^{2}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-80-36x+2x^{2}=1920$$

80 ni ikki tarafga qo’shing.

$$-36x+2x^{2}=1920+80$$

2000 olish uchun 1920 va 80'ni qo'shing.

$$-36x+2x^{2}=2000$$

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

$$2x^{2}-36x=2000$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-36x}{2}=\frac{2000}{2}$$

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

$$x^{2}+\left(-\frac{36}{2}\right)x=\frac{2000}{2}$$

-36 ni 2 ga bo'lish.

$$x^{2}-18x=\frac{2000}{2}$$

2000 ni 2 ga bo'lish.

$$x^{2}-18x=1000$$

-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.

$$x^{2}-18x+\left(-9\right)^{2}=1000+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=1000+81$$

1000 ni 81 ga qo'shish.

$$x^{2}-18x+81=1081$$

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.

$$\left(x-9\right)^{2}=1081$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{1081}$$

Qisqartirish.

$$x-9=\sqrt{1081} x-9=-\sqrt{1081}$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{1081}+9 x=9-\sqrt{1081}$$