(10+x)(800-20x)=12000 eching

$$(10+x)(800-20x)=12000$$

x uchun yechish

$$x=10$$

$$x=20$$

Kvadrat tenglamalaridan foydalanish qoidalari

10+x ga 800-20x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8000+600x-20x^{2}=12000$$

Ikkala tarafdan 12000 ni ayirish.

$$8000+600x-20x^{2}-12000=0$$

-4000 olish uchun 8000 dan 12000 ni ayirish.

$$-4000+600x-20x^{2}=0$$

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.

$$-20x^{2}+600x-4000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -20 ni a, 600 ni b va -4000 ni c bilan almashtiring.

$$x=\frac{-600±\sqrt{600^{2}-4\left(-20\right)\left(-4000\right)}}{2\left(-20\right)}$$

600 kvadratini chiqarish.

$$x=\frac{-600±\sqrt{360000-4\left(-20\right)\left(-4000\right)}}{2\left(-20\right)}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-600±\sqrt{360000+80\left(-4000\right)}}{2\left(-20\right)}$$

80 ni -4000 marotabaga ko'paytirish.

$$x=\frac{-600±\sqrt{360000-320000}}{2\left(-20\right)}$$

360000 ni -320000 ga qo'shish.

$$x=\frac{-600±\sqrt{40000}}{2\left(-20\right)}$$

40000 ning kvadrat ildizini chiqarish.

$$x=\frac{-600±200}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-600±200}{-40}$$

x=\frac{-600±200}{-40} tenglamasini yeching, bunda ± musbat. -600 ni 200 ga qo'shish.

$$x=-\frac{400}{-40}$$

-400 ni -40 ga bo'lish.

$$x=10$$

x=\frac{-600±200}{-40} tenglamasini yeching, bunda ± manfiy. -600 dan 200 ni ayirish.

$$x=-\frac{800}{-40}$$

-800 ni -40 ga bo'lish.

$$x=20$$

Tenglama yechildi.

$$x=10 x=20$$

Kvadratni yakunlash bo'yicha qadamlar

10+x ga 800-20x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$8000+600x-20x^{2}=12000$$

Ikkala tarafdan 8000 ni ayirish.

$$600x-20x^{2}=12000-8000$$

4000 olish uchun 12000 dan 8000 ni ayirish.

$$600x-20x^{2}=4000$$

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

$$-20x^{2}+600x=4000$$

Ikki tarafini -20 ga bo‘ling.

$$\frac{-20x^{2}+600x}{-20}=\frac{4000}{-20}$$

-20 ga bo'lish -20 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{600}{-20}x=\frac{4000}{-20}$$

600 ni -20 ga bo'lish.

$$x^{2}-30x=\frac{4000}{-20}$$

4000 ni -20 ga bo'lish.

$$x^{2}-30x=-200$$

-30 ni bo‘lish, x shartining koeffitsienti, 2 ga -15 olish uchun. Keyin, -15 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-30x+\left(-15\right)^{2}=-200+\left(-15\right)^{2}$$

-15 kvadratini chiqarish.

$$x^{2}-30x+225=-200+225$$

-200 ni 225 ga qo'shish.

$$x^{2}-30x+225=25$$

x^{2}-30x+225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-15\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-15\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-15=5 x-15=-5$$

15 ni tenglamaning ikkala tarafiga qo'shish.

$$x=20 x=10$$