(40-30+x)(600-10x)=10000 eching

$$( 40 - 30 + x ) ( 600 - 10 x ) = 10000$$

x uchun yechish

$$x=10$$

$$x=40$$

Kvadrat tenglamalaridan foydalanish qoidalari

10 olish uchun 40 dan 30 ni ayirish.

$$\left(10+x\right)\left(600-10x\right)=10000$$

10+x ga 600-10x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6000+500x-10x^{2}=10000$$

Ikkala tarafdan 10000 ni ayirish.

$$6000+500x-10x^{2}-10000=0$$

-4000 olish uchun 6000 dan 10000 ni ayirish.

$$-4000+500x-10x^{2}=0$$

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.

$$-10x^{2}+500x-4000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -10 ni a, 500 ni b va -4000 ni c bilan almashtiring.

$$x=\frac{-500±\sqrt{500^{2}-4\left(-10\right)\left(-4000\right)}}{2\left(-10\right)}$$

500 kvadratini chiqarish.

$$x=\frac{-500±\sqrt{250000-4\left(-10\right)\left(-4000\right)}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-500±\sqrt{250000+40\left(-4000\right)}}{2\left(-10\right)}$$

40 ni -4000 marotabaga ko'paytirish.

$$x=\frac{-500±\sqrt{250000-160000}}{2\left(-10\right)}$$

250000 ni -160000 ga qo'shish.

$$x=\frac{-500±\sqrt{90000}}{2\left(-10\right)}$$

90000 ning kvadrat ildizini chiqarish.

$$x=\frac{-500±300}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$x=\frac{-500±300}{-20}$$

x=\frac{-500±300}{-20} tenglamasini yeching, bunda ± musbat. -500 ni 300 ga qo'shish.

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

-200 ni -20 ga bo'lish.

$$x=10$$

x=\frac{-500±300}{-20} tenglamasini yeching, bunda ± manfiy. -500 dan 300 ni ayirish.

$$x=-\frac{800}{-20}$$

-800 ni -20 ga bo'lish.

$$x=40$$

Tenglama yechildi.

$$x=10 x=40$$

Kvadratni yakunlash bo'yicha qadamlar

10 olish uchun 40 dan 30 ni ayirish.

$$\left(10+x\right)\left(600-10x\right)=10000$$

10+x ga 600-10x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6000+500x-10x^{2}=10000$$

Ikkala tarafdan 6000 ni ayirish.

$$500x-10x^{2}=10000-6000$$

4000 olish uchun 10000 dan 6000 ni ayirish.

$$500x-10x^{2}=4000$$

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

$$-10x^{2}+500x=4000$$

Ikki tarafini -10 ga bo‘ling.

$$\frac{-10x^{2}+500x}{-10}=\frac{4000}{-10}$$

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

$$x^{2}+\frac{500}{-10}x=\frac{4000}{-10}$$

500 ni -10 ga bo'lish.

$$x^{2}-50x=\frac{4000}{-10}$$

4000 ni -10 ga bo'lish.

$$x^{2}-50x=-400$$

-50 ni bo‘lish, x shartining koeffitsienti, 2 ga -25 olish uchun. Keyin, -25 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-50x+\left(-25\right)^{2}=-400+\left(-25\right)^{2}$$

-25 kvadratini chiqarish.

$$x^{2}-50x+625=-400+625$$

-400 ni 625 ga qo'shish.

$$x^{2}-50x+625=225$$

x^{2}-50x+625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-25\right)^{2}=225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{225}$$

Qisqartirish.

$$x-25=15 x-25=-15$$

25 ni tenglamaning ikkala tarafiga qo'shish.

$$x=40 x=10$$