(10+x)(730-x)=1000 eching

$$( 10 + x ) ( 730 - x ) = 1000$$

x uchun yechish

$$x=30\sqrt{151}+360\approx 728,646171823$$

$$x=360-30\sqrt{151}\approx -8,646171823$$

Kvadrat tenglamalaridan foydalanish qoidalari

10+x ga 730-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$7300+720x-x^{2}=1000$$

Ikkala tarafdan 1000 ni ayirish.

$$7300+720x-x^{2}-1000=0$$

6300 olish uchun 7300 dan 1000 ni ayirish.

$$6300+720x-x^{2}=0$$

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.

$$-x^{2}+720x+6300=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 720 ni b va 6300 ni c bilan almashtiring.

$$x=\frac{-720±\sqrt{720^{2}-4\left(-1\right)\times 6300}}{2\left(-1\right)}$$

720 kvadratini chiqarish.

$$x=\frac{-720±\sqrt{518400-4\left(-1\right)\times 6300}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-720±\sqrt{518400+4\times 6300}}{2\left(-1\right)}$$

4 ni 6300 marotabaga ko'paytirish.

$$x=\frac{-720±\sqrt{518400+25200}}{2\left(-1\right)}$$

518400 ni 25200 ga qo'shish.

$$x=\frac{-720±\sqrt{543600}}{2\left(-1\right)}$$

543600 ning kvadrat ildizini chiqarish.

$$x=\frac{-720±60\sqrt{151}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-720±60\sqrt{151}}{-2}$$

x=\frac{-720±60\sqrt{151}}{-2} tenglamasini yeching, bunda ± musbat. -720 ni 60\sqrt{151} ga qo'shish.

$$x=\frac{60\sqrt{151}-720}{-2}$$

-720+60\sqrt{151} ni -2 ga bo'lish.

$$x=360-30\sqrt{151}$$

x=\frac{-720±60\sqrt{151}}{-2} tenglamasini yeching, bunda ± manfiy. -720 dan 60\sqrt{151} ni ayirish.

$$x=\frac{-60\sqrt{151}-720}{-2}$$

-720-60\sqrt{151} ni -2 ga bo'lish.

$$x=30\sqrt{151}+360$$

Tenglama yechildi.

$$x=360-30\sqrt{151} x=30\sqrt{151}+360$$

Kvadratni yakunlash bo'yicha qadamlar

10+x ga 730-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$7300+720x-x^{2}=1000$$

Ikkala tarafdan 7300 ni ayirish.

$$720x-x^{2}=1000-7300$$

-6300 olish uchun 1000 dan 7300 ni ayirish.

$$720x-x^{2}=-6300$$

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

$$-x^{2}+720x=-6300$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+720x}{-1}=-\frac{6300}{-1}$$

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

$$x^{2}+\frac{720}{-1}x=-\frac{6300}{-1}$$

720 ni -1 ga bo'lish.

$$x^{2}-720x=-\frac{6300}{-1}$$

-6300 ni -1 ga bo'lish.

$$x^{2}-720x=6300$$

-720 ni bo‘lish, x shartining koeffitsienti, 2 ga -360 olish uchun. Keyin, -360 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-720x+\left(-360\right)^{2}=6300+\left(-360\right)^{2}$$

-360 kvadratini chiqarish.

$$x^{2}-720x+129600=6300+129600$$

6300 ni 129600 ga qo'shish.

$$x^{2}-720x+129600=135900$$

x^{2}-720x+129600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-360\right)^{2}=135900$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-360\right)^{2}}=\sqrt{135900}$$

Qisqartirish.

$$x-360=30\sqrt{151} x-360=-30\sqrt{151}$$

360 ni tenglamaning ikkala tarafiga qo'shish.

$$x=30\sqrt{151}+360 x=360-30\sqrt{151}$$