x^2-115x=550 eching

$$x ^ { 2 } - 115 x = 550$$

x uchun yechish

$$x = \frac{5 \sqrt{617} + 115}{2} \approx 119,598711742$$

$$x=\frac{115-5\sqrt{617}}{2}\approx -4,598711742$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-115x=550$$

Tenglamaning ikkala tarafidan 550 ni ayirish.

$$x^{2}-115x-550=550-550$$

O‘zidan 550 ayirilsa 0 qoladi.

$$x^{2}-115x-550=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -115 ni b va -550 ni c bilan almashtiring.

$$x=\frac{-\left(-115\right)±\sqrt{\left(-115\right)^{2}-4\left(-550\right)}}{2}$$

-115 kvadratini chiqarish.

$$x=\frac{-\left(-115\right)±\sqrt{13225-4\left(-550\right)}}{2}$$

-4 ni -550 marotabaga ko'paytirish.

$$x=\frac{-\left(-115\right)±\sqrt{13225+2200}}{2}$$

13225 ni 2200 ga qo'shish.

$$x=\frac{-\left(-115\right)±\sqrt{15425}}{2}$$

15425 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-115\right)±5\sqrt{617}}{2}$$

-115 ning teskarisi 115 ga teng.

$$x=\frac{115±5\sqrt{617}}{2}$$

x=\frac{115±5\sqrt{617}}{2} tenglamasini yeching, bunda ± musbat. 115 ni 5\sqrt{617} ga qo'shish.

$$x=\frac{5\sqrt{617}+115}{2}$$

x=\frac{115±5\sqrt{617}}{2} tenglamasini yeching, bunda ± manfiy. 115 dan 5\sqrt{617} ni ayirish.

$$x=\frac{115-5\sqrt{617}}{2}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{617}+115}{2} x=\frac{115-5\sqrt{617}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}-115x=550$$

-115 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{115}{2} olish uchun. Keyin, -\frac{115}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-115x+\left(-\frac{115}{2}\right)^{2}=550+\left(-\frac{115}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{115}{2} kvadratini chiqarish.

$$x^{2}-115x+\frac{13225}{4}=550+\frac{13225}{4}$$

550 ni \frac{13225}{4} ga qo'shish.

$$x^{2}-115x+\frac{13225}{4}=\frac{15425}{4}$$

x^{2}-115x+\frac{13225}{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.

$$\left(x-\frac{115}{2}\right)^{2}=\frac{15425}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{115}{2}\right)^{2}}=\sqrt{\frac{15425}{4}}$$

Qisqartirish.

$$x-\frac{115}{2}=\frac{5\sqrt{617}}{2} x-\frac{115}{2}=-\frac{5\sqrt{617}}{2}$$

\frac{115}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{617}+115}{2} x=\frac{115-5\sqrt{617}}{2}$$