(100+x)(200-x)=20000 eching

$$( 100 + x ) ( 200 - x ) = 20000$$

x uchun yechish

$$x=100$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

100+x ga 200-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$20000+100x-x^{2}=20000$$

Ikkala tarafdan 20000 ni ayirish.

$$20000+100x-x^{2}-20000=0$$

0 olish uchun 20000 dan 20000 ni ayirish.

$$100x-x^{2}=0$$

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.

$$-x^{2}+100x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 100 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-100±\sqrt{100^{2}}}{2\left(-1\right)}$$

100^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-100±100}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-100±100}{-2}$$

x=\frac{-100±100}{-2} tenglamasini yeching, bunda ± musbat. -100 ni 100 ga qo'shish.

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

x=\frac{-100±100}{-2} tenglamasini yeching, bunda ± manfiy. -100 dan 100 ni ayirish.

$$x=-\frac{200}{-2}$$

-200 ni -2 ga bo'lish.

$$x=100$$

Tenglama yechildi.

$$x=0 x=100$$

Kvadratni yakunlash bo'yicha qadamlar

100+x ga 200-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$20000+100x-x^{2}=20000$$

Ikkala tarafdan 20000 ni ayirish.

$$100x-x^{2}=20000-20000$$

0 olish uchun 20000 dan 20000 ni ayirish.

$$100x-x^{2}=0$$

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

$$-x^{2}+100x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+100x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{100}{-1}x=\frac{0}{-1}$$

100 ni -1 ga bo'lish.

$$x^{2}-100x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}-100x=0$$

-100 ni bo‘lish, x shartining koeffitsienti, 2 ga -50 olish uchun. Keyin, -50 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-100x+\left(-50\right)^{2}=\left(-50\right)^{2}$$

-50 kvadratini chiqarish.

$$x^{2}-100x+2500=2500$$

x^{2}-100x+2500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-50\right)^{2}=2500$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{2500}$$

Qisqartirish.

$$x-50=50 x-50=-50$$

50 ni tenglamaning ikkala tarafiga qo'shish.

$$x=100 x=0$$