(50-40+x)(500-10x)=8000 eching

$$( 50 - 40 + x ) ( 500 - 10 x ) = 8000$$

x uchun yechish

$$x=10$$

$$x=30$$

Kvadrat tenglamalaridan foydalanish qoidalari

10 olish uchun 50 dan 40 ni ayirish.

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

10+x ga 500-10x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$5000+400x-10x^{2}=8000$$

Ikkala tarafdan 8000 ni ayirish.

$$5000+400x-10x^{2}-8000=0$$

-3000 olish uchun 5000 dan 8000 ni ayirish.

$$-3000+400x-10x^{2}=0$$

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.

$$-10x^{2}+400x-3000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -10 ni a, 400 ni b va -3000 ni c bilan almashtiring.

$$x=\frac{-400±\sqrt{400^{2}-4\left(-10\right)\left(-3000\right)}}{2\left(-10\right)}$$

400 kvadratini chiqarish.

$$x=\frac{-400±\sqrt{160000-4\left(-10\right)\left(-3000\right)}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-400±\sqrt{160000+40\left(-3000\right)}}{2\left(-10\right)}$$

40 ni -3000 marotabaga ko'paytirish.

$$x=\frac{-400±\sqrt{160000-120000}}{2\left(-10\right)}$$

160000 ni -120000 ga qo'shish.

$$x=\frac{-400±\sqrt{40000}}{2\left(-10\right)}$$

40000 ning kvadrat ildizini chiqarish.

$$x=\frac{-400±200}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$x=\frac{-400±200}{-20}$$

x=\frac{-400±200}{-20} tenglamasini yeching, bunda ± musbat. -400 ni 200 ga qo'shish.

$$x=-\frac{200}{-20}$$

-200 ni -20 ga bo'lish.

$$x=10$$

x=\frac{-400±200}{-20} tenglamasini yeching, bunda ± manfiy. -400 dan 200 ni ayirish.

$$x=-\frac{600}{-20}$$

-600 ni -20 ga bo'lish.

$$x=30$$

Tenglama yechildi.

$$x=10 x=30$$

Kvadratni yakunlash bo'yicha qadamlar

10 olish uchun 50 dan 40 ni ayirish.

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

10+x ga 500-10x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$5000+400x-10x^{2}=8000$$

Ikkala tarafdan 5000 ni ayirish.

$$400x-10x^{2}=8000-5000$$

3000 olish uchun 8000 dan 5000 ni ayirish.

$$400x-10x^{2}=3000$$

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

$$-10x^{2}+400x=3000$$

Ikki tarafini -10 ga bo‘ling.

$$\frac{-10x^{2}+400x}{-10}=\frac{3000}{-10}$$

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

$$x^{2}+\frac{400}{-10}x=\frac{3000}{-10}$$

400 ni -10 ga bo'lish.

$$x^{2}-40x=\frac{3000}{-10}$$

3000 ni -10 ga bo'lish.

$$x^{2}-40x=-300$$

-40 ni bo‘lish, x shartining koeffitsienti, 2 ga -20 olish uchun. Keyin, -20 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-40x+\left(-20\right)^{2}=-300+\left(-20\right)^{2}$$

-20 kvadratini chiqarish.

$$x^{2}-40x+400=-300+400$$

-300 ni 400 ga qo'shish.

$$x^{2}-40x+400=100$$

x^{2}-40x+400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-20\right)^{2}=100$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-20\right)^{2}}=\sqrt{100}$$

Qisqartirish.

$$x-20=10 x-20=-10$$

20 ni tenglamaning ikkala tarafiga qo'shish.

$$x=30 x=10$$