(100-x)*(30+x)=4200 eching

$$(100-x) \times (30+x)=4200$$

x uchun yechish

$$x=30$$

$$x=40$$

Kvadrat tenglamalaridan foydalanish qoidalari

100-x ga 30+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3000+70x-x^{2}=4200$$

Ikkala tarafdan 4200 ni ayirish.

$$3000+70x-x^{2}-4200=0$$

-1200 olish uchun 3000 dan 4200 ni ayirish.

$$-1200+70x-x^{2}=0$$

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.

$$-x^{2}+70x-1200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 70 ni b va -1200 ni c bilan almashtiring.

$$x=\frac{-70±\sqrt{70^{2}-4\left(-1\right)\left(-1200\right)}}{2\left(-1\right)}$$

70 kvadratini chiqarish.

$$x=\frac{-70±\sqrt{4900-4\left(-1\right)\left(-1200\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-70±\sqrt{4900+4\left(-1200\right)}}{2\left(-1\right)}$$

4 ni -1200 marotabaga ko'paytirish.

$$x=\frac{-70±\sqrt{4900-4800}}{2\left(-1\right)}$$

4900 ni -4800 ga qo'shish.

$$x=\frac{-70±\sqrt{100}}{2\left(-1\right)}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-70±10}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-70±10}{-2}$$

x=\frac{-70±10}{-2} tenglamasini yeching, bunda ± musbat. -70 ni 10 ga qo'shish.

$$x=-\frac{60}{-2}$$

-60 ni -2 ga bo'lish.

$$x=30$$

x=\frac{-70±10}{-2} tenglamasini yeching, bunda ± manfiy. -70 dan 10 ni ayirish.

$$x=-\frac{80}{-2}$$

-80 ni -2 ga bo'lish.

$$x=40$$

Tenglama yechildi.

$$x=30 x=40$$

Kvadratni yakunlash bo'yicha qadamlar

100-x ga 30+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3000+70x-x^{2}=4200$$

Ikkala tarafdan 3000 ni ayirish.

$$70x-x^{2}=4200-3000$$

1200 olish uchun 4200 dan 3000 ni ayirish.

$$70x-x^{2}=1200$$

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

$$-x^{2}+70x=1200$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+70x}{-1}=\frac{1200}{-1}$$

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

$$x^{2}+\frac{70}{-1}x=\frac{1200}{-1}$$

70 ni -1 ga bo'lish.

$$x^{2}-70x=\frac{1200}{-1}$$

1200 ni -1 ga bo'lish.

$$x^{2}-70x=-1200$$

-70 ni bo‘lish, x shartining koeffitsienti, 2 ga -35 olish uchun. Keyin, -35 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-70x+\left(-35\right)^{2}=-1200+\left(-35\right)^{2}$$

-35 kvadratini chiqarish.

$$x^{2}-70x+1225=-1200+1225$$

-1200 ni 1225 ga qo'shish.

$$x^{2}-70x+1225=25$$

x^{2}-70x+1225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-35\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-35\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-35=5 x-35=-5$$

35 ni tenglamaning ikkala tarafiga qo'shish.

$$x=40 x=30$$