(2(480-x)+160)(x-360)=20000 eching

$$(2(480-x)+160)(x-360)=20000$$

x uchun yechish

$$x=460$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 ga 480-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(960-2x+160\right)\left(x-360\right)=20000$$

1120 olish uchun 960 va 160'ni qo'shing.

$$\left(1120-2x\right)\left(x-360\right)=20000$$

1120-2x ifodaning har bir elementini x-360 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$1120x-403200-2x^{2}+720x=20000$$

1840x ni olish uchun 1120x va 720x ni birlashtirish.

$$1840x-403200-2x^{2}=20000$$

Ikkala tarafdan 20000 ni ayirish.

$$1840x-403200-2x^{2}-20000=0$$

-423200 olish uchun -403200 dan 20000 ni ayirish.

$$1840x-423200-2x^{2}=0$$

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.

$$-2x^{2}+1840x-423200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 1840 ni b va -423200 ni c bilan almashtiring.

$$x=\frac{-1840±\sqrt{1840^{2}-4\left(-2\right)\left(-423200\right)}}{2\left(-2\right)}$$

1840 kvadratini chiqarish.

$$x=\frac{-1840±\sqrt{3385600-4\left(-2\right)\left(-423200\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1840±\sqrt{3385600+8\left(-423200\right)}}{2\left(-2\right)}$$

8 ni -423200 marotabaga ko'paytirish.

$$x=\frac{-1840±\sqrt{3385600-3385600}}{2\left(-2\right)}$$

3385600 ni -3385600 ga qo'shish.

$$x=\frac{-1840±\sqrt{0}}{2\left(-2\right)}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{1840}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=-\frac{1840}{-4}$$

-1840 ni -4 ga bo'lish.

$$x=460$$

Kvadratni yakunlash bo'yicha qadamlar

2 ga 480-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(960-2x+160\right)\left(x-360\right)=20000$$

1120 olish uchun 960 va 160'ni qo'shing.

$$\left(1120-2x\right)\left(x-360\right)=20000$$

1120-2x ifodaning har bir elementini x-360 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$1120x-403200-2x^{2}+720x=20000$$

1840x ni olish uchun 1120x va 720x ni birlashtirish.

$$1840x-403200-2x^{2}=20000$$

403200 ni ikki tarafga qo’shing.

$$1840x-2x^{2}=20000+403200$$

423200 olish uchun 20000 va 403200'ni qo'shing.

$$1840x-2x^{2}=423200$$

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

$$-2x^{2}+1840x=423200$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+1840x}{-2}=\frac{423200}{-2}$$

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

$$x^{2}+\frac{1840}{-2}x=\frac{423200}{-2}$$

1840 ni -2 ga bo'lish.

$$x^{2}-920x=\frac{423200}{-2}$$

423200 ni -2 ga bo'lish.

$$x^{2}-920x=-211600$$

-920 ni bo‘lish, x shartining koeffitsienti, 2 ga -460 olish uchun. Keyin, -460 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-920x+\left(-460\right)^{2}=-211600+\left(-460\right)^{2}$$

-460 kvadratini chiqarish.

$$x^{2}-920x+211600=-211600+211600$$

-211600 ni 211600 ga qo'shish.

$$x^{2}-920x+211600=0$$

x^{2}-920x+211600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-460\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-460\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-460=0 x-460=0$$

460 ni tenglamaning ikkala tarafiga qo'shish.

$$x=460 x=460$$

Tenglama yechildi. Yechimlar bir xil.

$$x=460$$