(280-10x)x-6x=720 eching

$$( 280 - 10 x ) x - 6 x = 720$$

x uchun yechish

$$x = \frac{\sqrt{11569} + 137}{10} \approx 24,455928598$$

$$x = \frac{137 - \sqrt{11569}}{10} \approx 2,944071402$$

Kvadrat tenglamalaridan foydalanish qoidalari

280-10x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$280x-10x^{2}-6x=720$$

274x ni olish uchun 280x va -6x ni birlashtirish.

$$274x-10x^{2}=720$$

Ikkala tarafdan 720 ni ayirish.

$$274x-10x^{2}-720=0$$

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.

$$-10x^{2}+274x-720=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -10 ni a, 274 ni b va -720 ni c bilan almashtiring.

$$x=\frac{-274±\sqrt{274^{2}-4\left(-10\right)\left(-720\right)}}{2\left(-10\right)}$$

274 kvadratini chiqarish.

$$x=\frac{-274±\sqrt{75076-4\left(-10\right)\left(-720\right)}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-274±\sqrt{75076+40\left(-720\right)}}{2\left(-10\right)}$$

40 ni -720 marotabaga ko'paytirish.

$$x=\frac{-274±\sqrt{75076-28800}}{2\left(-10\right)}$$

75076 ni -28800 ga qo'shish.

$$x=\frac{-274±\sqrt{46276}}{2\left(-10\right)}$$

46276 ning kvadrat ildizini chiqarish.

$$x=\frac{-274±2\sqrt{11569}}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$x=\frac{-274±2\sqrt{11569}}{-20}$$

x=\frac{-274±2\sqrt{11569}}{-20} tenglamasini yeching, bunda ± musbat. -274 ni 2\sqrt{11569} ga qo'shish.

$$x=\frac{2\sqrt{11569}-274}{-20}$$

-274+2\sqrt{11569} ni -20 ga bo'lish.

$$x=\frac{137-\sqrt{11569}}{10}$$

x=\frac{-274±2\sqrt{11569}}{-20} tenglamasini yeching, bunda ± manfiy. -274 dan 2\sqrt{11569} ni ayirish.

$$x=\frac{-2\sqrt{11569}-274}{-20}$$

-274-2\sqrt{11569} ni -20 ga bo'lish.

$$x=\frac{\sqrt{11569}+137}{10}$$

Tenglama yechildi.

$$x=\frac{137-\sqrt{11569}}{10} x=\frac{\sqrt{11569}+137}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

280-10x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$280x-10x^{2}-6x=720$$

274x ni olish uchun 280x va -6x ni birlashtirish.

$$274x-10x^{2}=720$$

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

$$-10x^{2}+274x=720$$

Ikki tarafini -10 ga bo‘ling.

$$\frac{-10x^{2}+274x}{-10}=\frac{720}{-10}$$

-10 ga bo'lish -10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{274}{-10}x=\frac{720}{-10}$$

\frac{274}{-10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{137}{5}x=\frac{720}{-10}$$

720 ni -10 ga bo'lish.

$$x^{2}-\frac{137}{5}x=-72$$

-\frac{137}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{137}{10} olish uchun. Keyin, -\frac{137}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{137}{5}x+\left(-\frac{137}{10}\right)^{2}=-72+\left(-\frac{137}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{137}{10} kvadratini chiqarish.

$$x^{2}-\frac{137}{5}x+\frac{18769}{100}=-72+\frac{18769}{100}$$

-72 ni \frac{18769}{100} ga qo'shish.

$$x^{2}-\frac{137}{5}x+\frac{18769}{100}=\frac{11569}{100}$$

x^{2}-\frac{137}{5}x+\frac{18769}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{137}{10}\right)^{2}=\frac{11569}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{137}{10}\right)^{2}}=\sqrt{\frac{11569}{100}}$$

Qisqartirish.

$$x-\frac{137}{10}=\frac{\sqrt{11569}}{10} x-\frac{137}{10}=-\frac{\sqrt{11569}}{10}$$

\frac{137}{10} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{11569}+137}{10} x=\frac{137-\sqrt{11569}}{10}$$