-14/x+x=-17 eching

$$- \frac { 14 } { x } + x = - 17$$

x uchun yechish

$$x=\frac{\sqrt{345}-17}{2}\approx 0,787087811$$

$$x=\frac{-\sqrt{345}-17}{2}\approx -17,787087811$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$-14+xx=-17x$$

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

$$-14+x^{2}=-17x$$

17x ni ikki tarafga qo’shing.

$$-14+x^{2}+17x=0$$

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.

$$x^{2}+17x-14=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 17 ni b va -14 ni c bilan almashtiring.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-14\right)}}{2}$$

17 kvadratini chiqarish.

$$x=\frac{-17±\sqrt{289-4\left(-14\right)}}{2}$$

-4 ni -14 marotabaga ko'paytirish.

$$x=\frac{-17±\sqrt{289+56}}{2}$$

289 ni 56 ga qo'shish.

$$x=\frac{-17±\sqrt{345}}{2}$$

x=\frac{-17±\sqrt{345}}{2} tenglamasini yeching, bunda ± musbat. -17 ni \sqrt{345} ga qo'shish.

$$x=\frac{\sqrt{345}-17}{2}$$

x=\frac{-17±\sqrt{345}}{2} tenglamasini yeching, bunda ± manfiy. -17 dan \sqrt{345} ni ayirish.

$$x=\frac{-\sqrt{345}-17}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{345}-17}{2} x=\frac{-\sqrt{345}-17}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$-14+xx=-17x$$

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

$$-14+x^{2}=-17x$$

17x ni ikki tarafga qo’shing.

$$-14+x^{2}+17x=0$$

14 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+17x=14$$

17 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{17}{2} olish uchun. Keyin, \frac{17}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+17x+\left(\frac{17}{2}\right)^{2}=14+\left(\frac{17}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{17}{2} kvadratini chiqarish.

$$x^{2}+17x+\frac{289}{4}=14+\frac{289}{4}$$

14 ni \frac{289}{4} ga qo'shish.

$$x^{2}+17x+\frac{289}{4}=\frac{345}{4}$$

x^{2}+17x+\frac{289}{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.

$$\left(x+\frac{17}{2}\right)^{2}=\frac{345}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{17}{2}\right)^{2}}=\sqrt{\frac{345}{4}}$$

Qisqartirish.

$$x+\frac{17}{2}=\frac{\sqrt{345}}{2} x+\frac{17}{2}=-\frac{\sqrt{345}}{2}$$

Tenglamaning ikkala tarafidan \frac{17}{2} ni ayirish.

$$x=\frac{\sqrt{345}-17}{2} x=\frac{-\sqrt{345}-17}{2}$$