(40-x)(20+20x)=1200 eching

$$( 40 - x ) ( 20 + 20 x ) = 1200$$

x uchun yechish

$$x = \frac{\sqrt{1441} + 39}{2} \approx 38,480252896$$

$$x=\frac{39-\sqrt{1441}}{2}\approx 0,519747104$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$800+780x-20x^{2}=1200$$

Ikkala tarafdan 1200 ni ayirish.

$$800+780x-20x^{2}-1200=0$$

-400 olish uchun 800 dan 1200 ni ayirish.

$$-400+780x-20x^{2}=0$$

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.

$$-20x^{2}+780x-400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -20 ni a, 780 ni b va -400 ni c bilan almashtiring.

$$x=\frac{-780±\sqrt{780^{2}-4\left(-20\right)\left(-400\right)}}{2\left(-20\right)}$$

780 kvadratini chiqarish.

$$x=\frac{-780±\sqrt{608400-4\left(-20\right)\left(-400\right)}}{2\left(-20\right)}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-780±\sqrt{608400+80\left(-400\right)}}{2\left(-20\right)}$$

80 ni -400 marotabaga ko'paytirish.

$$x=\frac{-780±\sqrt{608400-32000}}{2\left(-20\right)}$$

608400 ni -32000 ga qo'shish.

$$x=\frac{-780±\sqrt{576400}}{2\left(-20\right)}$$

576400 ning kvadrat ildizini chiqarish.

$$x=\frac{-780±20\sqrt{1441}}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-780±20\sqrt{1441}}{-40}$$

x=\frac{-780±20\sqrt{1441}}{-40} tenglamasini yeching, bunda ± musbat. -780 ni 20\sqrt{1441} ga qo'shish.

$$x=\frac{20\sqrt{1441}-780}{-40}$$

-780+20\sqrt{1441} ni -40 ga bo'lish.

$$x=\frac{39-\sqrt{1441}}{2}$$

x=\frac{-780±20\sqrt{1441}}{-40} tenglamasini yeching, bunda ± manfiy. -780 dan 20\sqrt{1441} ni ayirish.

$$x=\frac{-20\sqrt{1441}-780}{-40}$$

-780-20\sqrt{1441} ni -40 ga bo'lish.

$$x=\frac{\sqrt{1441}+39}{2}$$

Tenglama yechildi.

$$x=\frac{39-\sqrt{1441}}{2} x=\frac{\sqrt{1441}+39}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$800+780x-20x^{2}=1200$$

Ikkala tarafdan 800 ni ayirish.

$$780x-20x^{2}=1200-800$$

400 olish uchun 1200 dan 800 ni ayirish.

$$780x-20x^{2}=400$$

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

$$-20x^{2}+780x=400$$

Ikki tarafini -20 ga bo‘ling.

$$\frac{-20x^{2}+780x}{-20}=\frac{400}{-20}$$

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

$$x^{2}+\frac{780}{-20}x=\frac{400}{-20}$$

780 ni -20 ga bo'lish.

$$x^{2}-39x=\frac{400}{-20}$$

400 ni -20 ga bo'lish.

$$x^{2}-39x=-20$$

-39 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{39}{2} olish uchun. Keyin, -\frac{39}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-39x+\left(-\frac{39}{2}\right)^{2}=-20+\left(-\frac{39}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{39}{2} kvadratini chiqarish.

$$x^{2}-39x+\frac{1521}{4}=-20+\frac{1521}{4}$$

-20 ni \frac{1521}{4} ga qo'shish.

$$x^{2}-39x+\frac{1521}{4}=\frac{1441}{4}$$

x^{2}-39x+\frac{1521}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{39}{2}\right)^{2}=\frac{1441}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{39}{2}\right)^{2}}=\sqrt{\frac{1441}{4}}$$

Qisqartirish.

$$x-\frac{39}{2}=\frac{\sqrt{1441}}{2} x-\frac{39}{2}=-\frac{\sqrt{1441}}{2}$$

\frac{39}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{1441}+39}{2} x=\frac{39-\sqrt{1441}}{2}$$