x^2-125x-375=0 eching

$$x ^ { 2 } - 125 x - 375 = 0$$

x uchun yechish

$$x = \frac{5 \sqrt{685} + 125}{2} \approx 127,931261642$$

$$x=\frac{125-5\sqrt{685}}{2}\approx -2,931261642$$

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.

$$x^{2}-125x-375=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -125 ni b va -375 ni c bilan almashtiring.

$$x=\frac{-\left(-125\right)±\sqrt{\left(-125\right)^{2}-4\left(-375\right)}}{2}$$

-125 kvadratini chiqarish.

$$x=\frac{-\left(-125\right)±\sqrt{15625-4\left(-375\right)}}{2}$$

-4 ni -375 marotabaga ko'paytirish.

$$x=\frac{-\left(-125\right)±\sqrt{15625+1500}}{2}$$

15625 ni 1500 ga qo'shish.

$$x=\frac{-\left(-125\right)±\sqrt{17125}}{2}$$

17125 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-125\right)±5\sqrt{685}}{2}$$

-125 ning teskarisi 125 ga teng.

$$x=\frac{125±5\sqrt{685}}{2}$$

x=\frac{125±5\sqrt{685}}{2} tenglamasini yeching, bunda ± musbat. 125 ni 5\sqrt{685} ga qo'shish.

$$x=\frac{5\sqrt{685}+125}{2}$$

x=\frac{125±5\sqrt{685}}{2} tenglamasini yeching, bunda ± manfiy. 125 dan 5\sqrt{685} ni ayirish.

$$x=\frac{125-5\sqrt{685}}{2}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{685}+125}{2} x=\frac{125-5\sqrt{685}}{2}$$

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.

$$x^{2}-125x-375=0$$

375 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-125x-375-\left(-375\right)=-\left(-375\right)$$

O‘zidan -375 ayirilsa 0 qoladi.

$$x^{2}-125x=-\left(-375\right)$$

0 dan -375 ni ayirish.

$$x^{2}-125x=375$$

-125 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{125}{2} olish uchun. Keyin, -\frac{125}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-125x+\left(-\frac{125}{2}\right)^{2}=375+\left(-\frac{125}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{125}{2} kvadratini chiqarish.

$$x^{2}-125x+\frac{15625}{4}=375+\frac{15625}{4}$$

375 ni \frac{15625}{4} ga qo'shish.

$$x^{2}-125x+\frac{15625}{4}=\frac{17125}{4}$$

x^{2}-125x+\frac{15625}{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.

$$\left(x-\frac{125}{2}\right)^{2}=\frac{17125}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{125}{2}\right)^{2}}=\sqrt{\frac{17125}{4}}$$

Qisqartirish.

$$x-\frac{125}{2}=\frac{5\sqrt{685}}{2} x-\frac{125}{2}=-\frac{5\sqrt{685}}{2}$$

\frac{125}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{685}+125}{2} x=\frac{125-5\sqrt{685}}{2}$$