E-1317=683:E= eching

$$E - 1317 = 683 : E =$$

E uchun yechish

$$E = \frac{\sqrt{1737221} + 1317}{2} \approx 1317,518398833$$

$$E=\frac{1317-\sqrt{1737221}}{2}\approx -0,518398833$$

Kvadrat tenglamalaridan foydalanish qoidalari

E qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini E ga ko'paytirish.

$$EE+E\left(-1317\right)=683$$

E^{2} hosil qilish uchun E va E ni ko'paytirish.

$$E^{2}+E\left(-1317\right)=683$$

Ikkala tarafdan 683 ni ayirish.

$$E^{2}+E\left(-1317\right)-683=0$$

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.

$$E^{2}-1317E-683=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1317 ni b va -683 ni c bilan almashtiring.

$$E=\frac{-\left(-1317\right)±\sqrt{\left(-1317\right)^{2}-4\left(-683\right)}}{2}$$

-1317 kvadratini chiqarish.

$$E=\frac{-\left(-1317\right)±\sqrt{1734489-4\left(-683\right)}}{2}$$

-4 ni -683 marotabaga ko'paytirish.

$$E=\frac{-\left(-1317\right)±\sqrt{1734489+2732}}{2}$$

1734489 ni 2732 ga qo'shish.

$$E=\frac{-\left(-1317\right)±\sqrt{1737221}}{2}$$

-1317 ning teskarisi 1317 ga teng.

$$E=\frac{1317±\sqrt{1737221}}{2}$$

E=\frac{1317±\sqrt{1737221}}{2} tenglamasini yeching, bunda ± musbat. 1317 ni \sqrt{1737221} ga qo'shish.

$$E=\frac{\sqrt{1737221}+1317}{2}$$

E=\frac{1317±\sqrt{1737221}}{2} tenglamasini yeching, bunda ± manfiy. 1317 dan \sqrt{1737221} ni ayirish.

$$E=\frac{1317-\sqrt{1737221}}{2}$$

Tenglama yechildi.

$$E=\frac{\sqrt{1737221}+1317}{2} E=\frac{1317-\sqrt{1737221}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

E qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini E ga ko'paytirish.

$$EE+E\left(-1317\right)=683$$

E^{2} hosil qilish uchun E va E ni ko'paytirish.

$$E^{2}+E\left(-1317\right)=683$$

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

$$E^{2}-1317E=683$$

-1317 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1317}{2} olish uchun. Keyin, -\frac{1317}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$E^{2}-1317E+\left(-\frac{1317}{2}\right)^{2}=683+\left(-\frac{1317}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1317}{2} kvadratini chiqarish.

$$E^{2}-1317E+\frac{1734489}{4}=683+\frac{1734489}{4}$$

683 ni \frac{1734489}{4} ga qo'shish.

$$E^{2}-1317E+\frac{1734489}{4}=\frac{1737221}{4}$$

E^{2}-1317E+\frac{1734489}{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.

$$\left(E-\frac{1317}{2}\right)^{2}=\frac{1737221}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(E-\frac{1317}{2}\right)^{2}}=\sqrt{\frac{1737221}{4}}$$

Qisqartirish.

$$E-\frac{1317}{2}=\frac{\sqrt{1737221}}{2} E-\frac{1317}{2}=-\frac{\sqrt{1737221}}{2}$$

\frac{1317}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$E=\frac{\sqrt{1737221}+1317}{2} E=\frac{1317-\sqrt{1737221}}{2}$$