x*(40-x)=381 eching

$$x \times ( 40 - x ) = 381$$

x uchun yechish

$$x=\sqrt{19}+20\approx 24,358898944$$

$$x=20-\sqrt{19}\approx 15,641101056$$

Kvadrat tenglamalaridan foydalanish qoidalari

x ga 40-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$40x-x^{2}=381$$

Ikkala tarafdan 381 ni ayirish.

$$40x-x^{2}-381=0$$

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.

$$-x^{2}+40x-381=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 40 ni b va -381 ni c bilan almashtiring.

$$x=\frac{-40±\sqrt{40^{2}-4\left(-1\right)\left(-381\right)}}{2\left(-1\right)}$$

40 kvadratini chiqarish.

$$x=\frac{-40±\sqrt{1600-4\left(-1\right)\left(-381\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-40±\sqrt{1600+4\left(-381\right)}}{2\left(-1\right)}$$

4 ni -381 marotabaga ko'paytirish.

$$x=\frac{-40±\sqrt{1600-1524}}{2\left(-1\right)}$$

1600 ni -1524 ga qo'shish.

$$x=\frac{-40±\sqrt{76}}{2\left(-1\right)}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-40±2\sqrt{19}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-40±2\sqrt{19}}{-2}$$

x=\frac{-40±2\sqrt{19}}{-2} tenglamasini yeching, bunda ± musbat. -40 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-40}{-2}$$

-40+2\sqrt{19} ni -2 ga bo'lish.

$$x=20-\sqrt{19}$$

x=\frac{-40±2\sqrt{19}}{-2} tenglamasini yeching, bunda ± manfiy. -40 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-40}{-2}$$

-40-2\sqrt{19} ni -2 ga bo'lish.

$$x=\sqrt{19}+20$$

Tenglama yechildi.

$$x=20-\sqrt{19} x=\sqrt{19}+20$$

Kvadratni yakunlash bo'yicha qadamlar

x ga 40-x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$40x-x^{2}=381$$

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

$$-x^{2}+40x=381$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+40x}{-1}=\frac{381}{-1}$$

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

$$x^{2}+\frac{40}{-1}x=\frac{381}{-1}$$

40 ni -1 ga bo'lish.

$$x^{2}-40x=\frac{381}{-1}$$

381 ni -1 ga bo'lish.

$$x^{2}-40x=-381$$

-40 ni bo‘lish, x shartining koeffitsienti, 2 ga -20 olish uchun. Keyin, -20 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-40x+\left(-20\right)^{2}=-381+\left(-20\right)^{2}$$

-20 kvadratini chiqarish.

$$x^{2}-40x+400=-381+400$$

-381 ni 400 ga qo'shish.

$$x^{2}-40x+400=19$$

x^{2}-40x+400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-20\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-20\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x-20=\sqrt{19} x-20=-\sqrt{19}$$

20 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{19}+20 x=20-\sqrt{19}$$