x^2+25x+7226=0 eching

$$x ^ { 2 } + 25 x + 7226 = 0$$

x uchun yechish (complex solution)

$$x=\frac{-25+\sqrt{28279}i}{2}\approx -12,5+84,081805404i$$

$$x=\frac{-\sqrt{28279}i-25}{2}\approx -12,5-84,081805404i$$

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.

$$x^{2}+25x+7226=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 25 ni b va 7226 ni c bilan almashtiring.

$$x=\frac{-25±\sqrt{25^{2}-4\times 7226}}{2}$$

25 kvadratini chiqarish.

$$x=\frac{-25±\sqrt{625-4\times 7226}}{2}$$

-4 ni 7226 marotabaga ko'paytirish.

$$x=\frac{-25±\sqrt{625-28904}}{2}$$

625 ni -28904 ga qo'shish.

$$x=\frac{-25±\sqrt{-28279}}{2}$$

-28279 ning kvadrat ildizini chiqarish.

$$x=\frac{-25±\sqrt{28279}i}{2}$$

x=\frac{-25±\sqrt{28279}i}{2} tenglamasini yeching, bunda ± musbat. -25 ni i\sqrt{28279} ga qo'shish.

$$x=\frac{-25+\sqrt{28279}i}{2}$$

x=\frac{-25±\sqrt{28279}i}{2} tenglamasini yeching, bunda ± manfiy. -25 dan i\sqrt{28279} ni ayirish.

$$x=\frac{-\sqrt{28279}i-25}{2}$$

Tenglama yechildi.

$$x=\frac{-25+\sqrt{28279}i}{2} x=\frac{-\sqrt{28279}i-25}{2}$$

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.

$$x^{2}+25x+7226=0$$

Tenglamaning ikkala tarafidan 7226 ni ayirish.

$$x^{2}+25x+7226-7226=-7226$$

O‘zidan 7226 ayirilsa 0 qoladi.

$$x^{2}+25x=-7226$$

25 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{25}{2} olish uchun. Keyin, \frac{25}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+25x+\left(\frac{25}{2}\right)^{2}=-7226+\left(\frac{25}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{25}{2} kvadratini chiqarish.

$$x^{2}+25x+\frac{625}{4}=-7226+\frac{625}{4}$$

-7226 ni \frac{625}{4} ga qo'shish.

$$x^{2}+25x+\frac{625}{4}=-\frac{28279}{4}$$

x^{2}+25x+\frac{625}{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.

$$\left(x+\frac{25}{2}\right)^{2}=-\frac{28279}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{25}{2}\right)^{2}}=\sqrt{-\frac{28279}{4}}$$

Qisqartirish.

$$x+\frac{25}{2}=\frac{\sqrt{28279}i}{2} x+\frac{25}{2}=-\frac{\sqrt{28279}i}{2}$$

Tenglamaning ikkala tarafidan \frac{25}{2} ni ayirish.

$$x=\frac{-25+\sqrt{28279}i}{2} x=\frac{-\sqrt{28279}i-25}{2}$$