-500a^2+53000a=600000 eching

$$-500 { a }^{ 2 } +53000a = 600000$$

a uchun yechish

$$a=\sqrt{1609}+53\approx 93,11234224$$

$$a=53-\sqrt{1609}\approx 12,88765776$$

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.

$$-500a^{2}+53000a=600000$$

Tenglamaning ikkala tarafidan 600000 ni ayirish.

$$-500a^{2}+53000a-600000=600000-600000$$

O‘zidan 600000 ayirilsa 0 qoladi.

$$-500a^{2}+53000a-600000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -500 ni a, 53000 ni b va -600000 ni c bilan almashtiring.

$$a=\frac{-53000±\sqrt{53000^{2}-4\left(-500\right)\left(-600000\right)}}{2\left(-500\right)}$$

53000 kvadratini chiqarish.

$$a=\frac{-53000±\sqrt{2809000000-4\left(-500\right)\left(-600000\right)}}{2\left(-500\right)}$$

-4 ni -500 marotabaga ko'paytirish.

$$a=\frac{-53000±\sqrt{2809000000+2000\left(-600000\right)}}{2\left(-500\right)}$$

2000 ni -600000 marotabaga ko'paytirish.

$$a=\frac{-53000±\sqrt{2809000000-1200000000}}{2\left(-500\right)}$$

2809000000 ni -1200000000 ga qo'shish.

$$a=\frac{-53000±\sqrt{1609000000}}{2\left(-500\right)}$$

1609000000 ning kvadrat ildizini chiqarish.

$$a=\frac{-53000±1000\sqrt{1609}}{2\left(-500\right)}$$

2 ni -500 marotabaga ko'paytirish.

$$a=\frac{-53000±1000\sqrt{1609}}{-1000}$$

a=\frac{-53000±1000\sqrt{1609}}{-1000} tenglamasini yeching, bunda ± musbat. -53000 ni 1000\sqrt{1609} ga qo'shish.

$$a=\frac{1000\sqrt{1609}-53000}{-1000}$$

-53000+1000\sqrt{1609} ni -1000 ga bo'lish.

$$a=53-\sqrt{1609}$$

a=\frac{-53000±1000\sqrt{1609}}{-1000} tenglamasini yeching, bunda ± manfiy. -53000 dan 1000\sqrt{1609} ni ayirish.

$$a=\frac{-1000\sqrt{1609}-53000}{-1000}$$

-53000-1000\sqrt{1609} ni -1000 ga bo'lish.

$$a=\sqrt{1609}+53$$

Tenglama yechildi.

$$a=53-\sqrt{1609} a=\sqrt{1609}+53$$

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.

$$-500a^{2}+53000a=600000$$

Ikki tarafini -500 ga bo‘ling.

$$\frac{-500a^{2}+53000a}{-500}=\frac{600000}{-500}$$

-500 ga bo'lish -500 ga ko'paytirishni bekor qiladi.

$$a^{2}+\frac{53000}{-500}a=\frac{600000}{-500}$$

53000 ni -500 ga bo'lish.

$$a^{2}-106a=\frac{600000}{-500}$$

600000 ni -500 ga bo'lish.

$$a^{2}-106a=-1200$$

-106 ni bo‘lish, x shartining koeffitsienti, 2 ga -53 olish uchun. Keyin, -53 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-106a+\left(-53\right)^{2}=-1200+\left(-53\right)^{2}$$

-53 kvadratini chiqarish.

$$a^{2}-106a+2809=-1200+2809$$

-1200 ni 2809 ga qo'shish.

$$a^{2}-106a+2809=1609$$

a^{2}-106a+2809 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a-53\right)^{2}=1609$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-53\right)^{2}}=\sqrt{1609}$$

Qisqartirish.

$$a-53=\sqrt{1609} a-53=-\sqrt{1609}$$

53 ni tenglamaning ikkala tarafiga qo'shish.

$$a=\sqrt{1609}+53 a=53-\sqrt{1609}$$