x^2=113*113-113x eching

$$x ^ { 2 } = 113 \times 113 - 113 x$$

x uchun yechish

$$x = \frac{113 \sqrt{5} - 113}{2} \approx 69,837840729$$

$$x=\frac{-113\sqrt{5}-113}{2}\approx -182,837840729$$

Kvadrat tenglamalaridan foydalanish qoidalari

12769 hosil qilish uchun 113 va 113 ni ko'paytirish.

$$x^{2}=12769-113x$$

Ikkala tarafdan 12769 ni ayirish.

$$x^{2}-12769=-113x$$

113x ni ikki tarafga qo’shing.

$$x^{2}-12769+113x=0$$

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.

$$x^{2}+113x-12769=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 113 ni b va -12769 ni c bilan almashtiring.

$$x=\frac{-113±\sqrt{113^{2}-4\left(-12769\right)}}{2}$$

113 kvadratini chiqarish.

$$x=\frac{-113±\sqrt{12769-4\left(-12769\right)}}{2}$$

-4 ni -12769 marotabaga ko'paytirish.

$$x=\frac{-113±\sqrt{12769+51076}}{2}$$

12769 ni 51076 ga qo'shish.

$$x=\frac{-113±\sqrt{63845}}{2}$$

63845 ning kvadrat ildizini chiqarish.

$$x=\frac{-113±113\sqrt{5}}{2}$$

x=\frac{-113±113\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. -113 ni 113\sqrt{5} ga qo'shish.

$$x=\frac{113\sqrt{5}-113}{2}$$

x=\frac{-113±113\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. -113 dan 113\sqrt{5} ni ayirish.

$$x=\frac{-113\sqrt{5}-113}{2}$$

Tenglama yechildi.

$$x=\frac{113\sqrt{5}-113}{2} x=\frac{-113\sqrt{5}-113}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

12769 hosil qilish uchun 113 va 113 ni ko'paytirish.

$$x^{2}=12769-113x$$

113x ni ikki tarafga qo’shing.

$$x^{2}+113x=12769$$

113 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{113}{2} olish uchun. Keyin, \frac{113}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+113x+\left(\frac{113}{2}\right)^{2}=12769+\left(\frac{113}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{113}{2} kvadratini chiqarish.

$$x^{2}+113x+\frac{12769}{4}=12769+\frac{12769}{4}$$

12769 ni \frac{12769}{4} ga qo'shish.

$$x^{2}+113x+\frac{12769}{4}=\frac{63845}{4}$$

x^{2}+113x+\frac{12769}{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.

$$\left(x+\frac{113}{2}\right)^{2}=\frac{63845}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{113}{2}\right)^{2}}=\sqrt{\frac{63845}{4}}$$

Qisqartirish.

$$x+\frac{113}{2}=\frac{113\sqrt{5}}{2} x+\frac{113}{2}=-\frac{113\sqrt{5}}{2}$$

Tenglamaning ikkala tarafidan \frac{113}{2} ni ayirish.

$$x=\frac{113\sqrt{5}-113}{2} x=\frac{-113\sqrt{5}-113}{2}$$