x^2-15000x+50000=0 eching

$$x ^ { 2 } - 15000 x + 50000 = 0$$

x uchun yechish

$$x=200\sqrt{1405}+7500\approx 14996,665925597$$

$$x=7500-200\sqrt{1405}\approx 3,334074403$$

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.

$$x^{2}-15000x+50000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -15000 ni b va 50000 ni c bilan almashtiring.

$$x=\frac{-\left(-15000\right)±\sqrt{\left(-15000\right)^{2}-4\times 50000}}{2}$$

-15000 kvadratini chiqarish.

$$x=\frac{-\left(-15000\right)±\sqrt{225000000-4\times 50000}}{2}$$

-4 ni 50000 marotabaga ko'paytirish.

$$x=\frac{-\left(-15000\right)±\sqrt{225000000-200000}}{2}$$

225000000 ni -200000 ga qo'shish.

$$x=\frac{-\left(-15000\right)±\sqrt{224800000}}{2}$$

224800000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15000\right)±400\sqrt{1405}}{2}$$

-15000 ning teskarisi 15000 ga teng.

$$x=\frac{15000±400\sqrt{1405}}{2}$$

x=\frac{15000±400\sqrt{1405}}{2} tenglamasini yeching, bunda ± musbat. 15000 ni 400\sqrt{1405} ga qo'shish.

$$x=\frac{400\sqrt{1405}+15000}{2}$$

15000+400\sqrt{1405} ni 2 ga bo'lish.

$$x=200\sqrt{1405}+7500$$

x=\frac{15000±400\sqrt{1405}}{2} tenglamasini yeching, bunda ± manfiy. 15000 dan 400\sqrt{1405} ni ayirish.

$$x=\frac{15000-400\sqrt{1405}}{2}$$

15000-400\sqrt{1405} ni 2 ga bo'lish.

$$x=7500-200\sqrt{1405}$$

Tenglama yechildi.

$$x=200\sqrt{1405}+7500 x=7500-200\sqrt{1405}$$

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.

$$x^{2}-15000x+50000=0$$

Tenglamaning ikkala tarafidan 50000 ni ayirish.

$$x^{2}-15000x+50000-50000=-50000$$

O‘zidan 50000 ayirilsa 0 qoladi.

$$x^{2}-15000x=-50000$$

-15000 ni bo‘lish, x shartining koeffitsienti, 2 ga -7500 olish uchun. Keyin, -7500 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-15000x+\left(-7500\right)^{2}=-50000+\left(-7500\right)^{2}$$

-7500 kvadratini chiqarish.

$$x^{2}-15000x+56250000=-50000+56250000$$

-50000 ni 56250000 ga qo'shish.

$$x^{2}-15000x+56250000=56200000$$

x^{2}-15000x+56250000 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-7500\right)^{2}=56200000$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-7500\right)^{2}}=\sqrt{56200000}$$

Qisqartirish.

$$x-7500=200\sqrt{1405} x-7500=-200\sqrt{1405}$$

7500 ni tenglamaning ikkala tarafiga qo'shish.

$$x=200\sqrt{1405}+7500 x=7500-200\sqrt{1405}$$