(x-40)[500-(x-50)*10]=8000 eching

$$( x - 40 ) [ 500 - ( x - 50 ) \times 10 ] = 8000$$

x uchun yechish

$$x=60$$

$$x=80$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-50 ga 10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x-40\right)\left(500-\left(10x-500\right)\right)=8000$$

10x-500 teskarisini topish uchun har birining teskarisini toping.

$$\left(x-40\right)\left(500-10x-\left(-500\right)\right)=8000$$

-500 ning teskarisi 500 ga teng.

$$\left(x-40\right)\left(500-10x+500\right)=8000$$

1000 olish uchun 500 va 500'ni qo'shing.

$$\left(x-40\right)\left(1000-10x\right)=8000$$

x-40 ifodaning har bir elementini 1000-10x ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$1000x-10x^{2}-40000+400x=8000$$

1400x ni olish uchun 1000x va 400x ni birlashtirish.

$$1400x-10x^{2}-40000=8000$$

Ikkala tarafdan 8000 ni ayirish.

$$1400x-10x^{2}-40000-8000=0$$

-48000 olish uchun -40000 dan 8000 ni ayirish.

$$1400x-10x^{2}-48000=0$$

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.

$$-10x^{2}+1400x-48000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -10 ni a, 1400 ni b va -48000 ni c bilan almashtiring.

$$x=\frac{-1400±\sqrt{1400^{2}-4\left(-10\right)\left(-48000\right)}}{2\left(-10\right)}$$

1400 kvadratini chiqarish.

$$x=\frac{-1400±\sqrt{1960000-4\left(-10\right)\left(-48000\right)}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-1400±\sqrt{1960000+40\left(-48000\right)}}{2\left(-10\right)}$$

40 ni -48000 marotabaga ko'paytirish.

$$x=\frac{-1400±\sqrt{1960000-1920000}}{2\left(-10\right)}$$

1960000 ni -1920000 ga qo'shish.

$$x=\frac{-1400±\sqrt{40000}}{2\left(-10\right)}$$

40000 ning kvadrat ildizini chiqarish.

$$x=\frac{-1400±200}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$x=\frac{-1400±200}{-20}$$

x=\frac{-1400±200}{-20} tenglamasini yeching, bunda ± musbat. -1400 ni 200 ga qo'shish.

$$x=-\frac{1200}{-20}$$

-1200 ni -20 ga bo'lish.

$$x=60$$

x=\frac{-1400±200}{-20} tenglamasini yeching, bunda ± manfiy. -1400 dan 200 ni ayirish.

$$x=-\frac{1600}{-20}$$

-1600 ni -20 ga bo'lish.

$$x=80$$

Tenglama yechildi.

$$x=60 x=80$$

Kvadratni yakunlash bo'yicha qadamlar

x-50 ga 10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(x-40\right)\left(500-\left(10x-500\right)\right)=8000$$

10x-500 teskarisini topish uchun har birining teskarisini toping.

$$\left(x-40\right)\left(500-10x-\left(-500\right)\right)=8000$$

-500 ning teskarisi 500 ga teng.

$$\left(x-40\right)\left(500-10x+500\right)=8000$$

1000 olish uchun 500 va 500'ni qo'shing.

$$\left(x-40\right)\left(1000-10x\right)=8000$$

x-40 ifodaning har bir elementini 1000-10x ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$1000x-10x^{2}-40000+400x=8000$$

1400x ni olish uchun 1000x va 400x ni birlashtirish.

$$1400x-10x^{2}-40000=8000$$

40000 ni ikki tarafga qo’shing.

$$1400x-10x^{2}=8000+40000$$

48000 olish uchun 8000 va 40000'ni qo'shing.

$$1400x-10x^{2}=48000$$

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

$$-10x^{2}+1400x=48000$$

Ikki tarafini -10 ga bo‘ling.

$$\frac{-10x^{2}+1400x}{-10}=\frac{48000}{-10}$$

-10 ga bo'lish -10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1400}{-10}x=\frac{48000}{-10}$$

1400 ni -10 ga bo'lish.

$$x^{2}-140x=\frac{48000}{-10}$$

48000 ni -10 ga bo'lish.

$$x^{2}-140x=-4800$$

-140 ni bo‘lish, x shartining koeffitsienti, 2 ga -70 olish uchun. Keyin, -70 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-140x+\left(-70\right)^{2}=-4800+\left(-70\right)^{2}$$

-70 kvadratini chiqarish.

$$x^{2}-140x+4900=-4800+4900$$

-4800 ni 4900 ga qo'shish.

$$x^{2}-140x+4900=100$$

x^{2}-140x+4900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-70\right)^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-70\right)^{2}}=\sqrt{100}$$

Qisqartirish.

$$x-70=10 x-70=-10$$

70 ni tenglamaning ikkala tarafiga qo'shish.

$$x=80 x=60$$