x^2+3394*x+3976=0 eching

$${ x }^{ 2 } +3394 \times x+3976=0$$

x uchun yechish

$$x=3\sqrt{319537}-1697\approx -1,17188371$$

$$x=-3\sqrt{319537}-1697\approx -3392,82811629$$

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.

$$x^{2}+3394x+3976=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 3394 ni b va 3976 ni c bilan almashtiring.

$$x=\frac{-3394±\sqrt{3394^{2}-4\times 3976}}{2}$$

3394 kvadratini chiqarish.

$$x=\frac{-3394±\sqrt{11519236-4\times 3976}}{2}$$

-4 ni 3976 marotabaga ko'paytirish.

$$x=\frac{-3394±\sqrt{11519236-15904}}{2}$$

11519236 ni -15904 ga qo'shish.

$$x=\frac{-3394±\sqrt{11503332}}{2}$$

11503332 ning kvadrat ildizini chiqarish.

$$x=\frac{-3394±6\sqrt{319537}}{2}$$

x=\frac{-3394±6\sqrt{319537}}{2} tenglamasini yeching, bunda ± musbat. -3394 ni 6\sqrt{319537} ga qo'shish.

$$x=\frac{6\sqrt{319537}-3394}{2}$$

-3394+6\sqrt{319537} ni 2 ga bo'lish.

$$x=3\sqrt{319537}-1697$$

x=\frac{-3394±6\sqrt{319537}}{2} tenglamasini yeching, bunda ± manfiy. -3394 dan 6\sqrt{319537} ni ayirish.

$$x=\frac{-6\sqrt{319537}-3394}{2}$$

-3394-6\sqrt{319537} ni 2 ga bo'lish.

$$x=-3\sqrt{319537}-1697$$

Tenglama yechildi.

$$x=3\sqrt{319537}-1697 x=-3\sqrt{319537}-1697$$

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.

$$x^{2}+3394x+3976=0$$

Tenglamaning ikkala tarafidan 3976 ni ayirish.

$$x^{2}+3394x+3976-3976=-3976$$

O‘zidan 3976 ayirilsa 0 qoladi.

$$x^{2}+3394x=-3976$$

3394 ni bo‘lish, x shartining koeffitsienti, 2 ga 1697 olish uchun. Keyin, 1697 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+3394x+1697^{2}=-3976+1697^{2}$$

1697 kvadratini chiqarish.

$$x^{2}+3394x+2879809=-3976+2879809$$

-3976 ni 2879809 ga qo'shish.

$$x^{2}+3394x+2879809=2875833$$

x^{2}+3394x+2879809 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1697\right)^{2}=2875833$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1697\right)^{2}}=\sqrt{2875833}$$

Qisqartirish.

$$x+1697=3\sqrt{319537} x+1697=-3\sqrt{319537}$$

Tenglamaning ikkala tarafidan 1697 ni ayirish.

$$x=3\sqrt{319537}-1697 x=-3\sqrt{319537}-1697$$