x^2-379x-188=303 eching

$$x ^ { 2 } - 379 x - 188 = 303$$

x uchun yechish

$$x = \frac{\sqrt{145605} + 379}{2} \approx 380,291116145$$

$$x=\frac{379-\sqrt{145605}}{2}\approx -1,291116145$$

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.

$$x^{2}-379x-188=303$$

Tenglamaning ikkala tarafidan 303 ni ayirish.

$$x^{2}-379x-188-303=303-303$$

O‘zidan 303 ayirilsa 0 qoladi.

$$x^{2}-379x-188-303=0$$

-188 dan 303 ni ayirish.

$$x^{2}-379x-491=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -379 ni b va -491 ni c bilan almashtiring.

$$x=\frac{-\left(-379\right)±\sqrt{\left(-379\right)^{2}-4\left(-491\right)}}{2}$$

-379 kvadratini chiqarish.

$$x=\frac{-\left(-379\right)±\sqrt{143641-4\left(-491\right)}}{2}$$

-4 ni -491 marotabaga ko'paytirish.

$$x=\frac{-\left(-379\right)±\sqrt{143641+1964}}{2}$$

143641 ni 1964 ga qo'shish.

$$x=\frac{-\left(-379\right)±\sqrt{145605}}{2}$$

-379 ning teskarisi 379 ga teng.

$$x=\frac{379±\sqrt{145605}}{2}$$

x=\frac{379±\sqrt{145605}}{2} tenglamasini yeching, bunda ± musbat. 379 ni \sqrt{145605} ga qo'shish.

$$x=\frac{\sqrt{145605}+379}{2}$$

x=\frac{379±\sqrt{145605}}{2} tenglamasini yeching, bunda ± manfiy. 379 dan \sqrt{145605} ni ayirish.

$$x=\frac{379-\sqrt{145605}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{145605}+379}{2} x=\frac{379-\sqrt{145605}}{2}$$

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.

$$x^{2}-379x-188=303$$

188 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-379x-188-\left(-188\right)=303-\left(-188\right)$$

O‘zidan -188 ayirilsa 0 qoladi.

$$x^{2}-379x=303-\left(-188\right)$$

303 dan -188 ni ayirish.

$$x^{2}-379x=491$$

-379 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{379}{2} olish uchun. Keyin, -\frac{379}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-379x+\left(-\frac{379}{2}\right)^{2}=491+\left(-\frac{379}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{379}{2} kvadratini chiqarish.

$$x^{2}-379x+\frac{143641}{4}=491+\frac{143641}{4}$$

491 ni \frac{143641}{4} ga qo'shish.

$$x^{2}-379x+\frac{143641}{4}=\frac{145605}{4}$$

x^{2}-379x+\frac{143641}{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.

$$\left(x-\frac{379}{2}\right)^{2}=\frac{145605}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{379}{2}\right)^{2}}=\sqrt{\frac{145605}{4}}$$

Qisqartirish.

$$x-\frac{379}{2}=\frac{\sqrt{145605}}{2} x-\frac{379}{2}=-\frac{\sqrt{145605}}{2}$$

\frac{379}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{145605}+379}{2} x=\frac{379-\sqrt{145605}}{2}$$