(x)=212x-5000-x^2 eching

$$( x ) = 212 x - 5000 - x ^ { 2 }$$

x uchun yechish

$$x = \frac{\sqrt{24521} + 211}{2} \approx 183,795913048$$

$$x = \frac{211 - \sqrt{24521}}{2} \approx 27,204086952$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 212x ni ayirish.

$$x-212x=-5000-x^{2}$$

-211x ni olish uchun x va -212x ni birlashtirish.

$$-211x=-5000-x^{2}$$

Ikkala tarafdan -5000 ni ayirish.

$$-211x-\left(-5000\right)=-x^{2}$$

-5000 ning teskarisi 5000 ga teng.

$$-211x+5000=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$-211x+5000+x^{2}=0$$

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.

$$x^{2}-211x+5000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -211 ni b va 5000 ni c bilan almashtiring.

$$x=\frac{-\left(-211\right)±\sqrt{\left(-211\right)^{2}-4\times 5000}}{2}$$

-211 kvadratini chiqarish.

$$x=\frac{-\left(-211\right)±\sqrt{44521-4\times 5000}}{2}$$

-4 ni 5000 marotabaga ko'paytirish.

$$x=\frac{-\left(-211\right)±\sqrt{44521-20000}}{2}$$

44521 ni -20000 ga qo'shish.

$$x=\frac{-\left(-211\right)±\sqrt{24521}}{2}$$

-211 ning teskarisi 211 ga teng.

$$x=\frac{211±\sqrt{24521}}{2}$$

x=\frac{211±\sqrt{24521}}{2} tenglamasini yeching, bunda ± musbat. 211 ni \sqrt{24521} ga qo'shish.

$$x=\frac{\sqrt{24521}+211}{2}$$

x=\frac{211±\sqrt{24521}}{2} tenglamasini yeching, bunda ± manfiy. 211 dan \sqrt{24521} ni ayirish.

$$x=\frac{211-\sqrt{24521}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{24521}+211}{2} x=\frac{211-\sqrt{24521}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 212x ni ayirish.

$$x-212x=-5000-x^{2}$$

-211x ni olish uchun x va -212x ni birlashtirish.

$$-211x=-5000-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$-211x+x^{2}=-5000$$

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

$$x^{2}-211x=-5000$$

-211 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{211}{2} olish uchun. Keyin, -\frac{211}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-211x+\left(-\frac{211}{2}\right)^{2}=-5000+\left(-\frac{211}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{211}{2} kvadratini chiqarish.

$$x^{2}-211x+\frac{44521}{4}=-5000+\frac{44521}{4}$$

-5000 ni \frac{44521}{4} ga qo'shish.

$$x^{2}-211x+\frac{44521}{4}=\frac{24521}{4}$$

x^{2}-211x+\frac{44521}{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.

$$\left(x-\frac{211}{2}\right)^{2}=\frac{24521}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{211}{2}\right)^{2}}=\sqrt{\frac{24521}{4}}$$

Qisqartirish.

$$x-\frac{211}{2}=\frac{\sqrt{24521}}{2} x-\frac{211}{2}=-\frac{\sqrt{24521}}{2}$$

\frac{211}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{24521}+211}{2} x=\frac{211-\sqrt{24521}}{2}$$