x^2-12500x+6=0 eching

$$x ^ { 2 } - 12500 x + 6 = 0$$

x uchun yechish

$$x=\sqrt{39062494}+6250\approx 12499,99952$$

$$x=6250-\sqrt{39062494}\approx 0,00048$$

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.

$$x^{2}-12500x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12500 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-12500\right)±\sqrt{\left(-12500\right)^{2}-4\times 6}}{2}$$

-12500 kvadratini chiqarish.

$$x=\frac{-\left(-12500\right)±\sqrt{156250000-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-12500\right)±\sqrt{156250000-24}}{2}$$

156250000 ni -24 ga qo'shish.

$$x=\frac{-\left(-12500\right)±\sqrt{156249976}}{2}$$

156249976 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12500\right)±2\sqrt{39062494}}{2}$$

-12500 ning teskarisi 12500 ga teng.

$$x=\frac{12500±2\sqrt{39062494}}{2}$$

x=\frac{12500±2\sqrt{39062494}}{2} tenglamasini yeching, bunda ± musbat. 12500 ni 2\sqrt{39062494} ga qo'shish.

$$x=\frac{2\sqrt{39062494}+12500}{2}$$

12500+2\sqrt{39062494} ni 2 ga bo'lish.

$$x=\sqrt{39062494}+6250$$

x=\frac{12500±2\sqrt{39062494}}{2} tenglamasini yeching, bunda ± manfiy. 12500 dan 2\sqrt{39062494} ni ayirish.

$$x=\frac{12500-2\sqrt{39062494}}{2}$$

12500-2\sqrt{39062494} ni 2 ga bo'lish.

$$x=6250-\sqrt{39062494}$$

Tenglama yechildi.

$$x=\sqrt{39062494}+6250 x=6250-\sqrt{39062494}$$

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.

$$x^{2}-12500x+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x^{2}-12500x+6-6=-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$x^{2}-12500x=-6$$

-12500 ni bo‘lish, x shartining koeffitsienti, 2 ga -6250 olish uchun. Keyin, -6250 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12500x+\left(-6250\right)^{2}=-6+\left(-6250\right)^{2}$$

-6250 kvadratini chiqarish.

$$x^{2}-12500x+39062500=-6+39062500$$

-6 ni 39062500 ga qo'shish.

$$x^{2}-12500x+39062500=39062494$$

x^{2}-12500x+39062500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6250\right)^{2}=39062494$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6250\right)^{2}}=\sqrt{39062494}$$

Qisqartirish.

$$x-6250=\sqrt{39062494} x-6250=-\sqrt{39062494}$$

6250 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{39062494}+6250 x=6250-\sqrt{39062494}$$