2x^2-5000x+9000=0 eching

$$2 x ^ { 2 } - 5000 x + 9000 = 0$$

x uchun yechish

$$x=20\sqrt{3895}+1250\approx 2498,19870213$$

$$x=1250-20\sqrt{3895}\approx 1,80129787$$

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.

$$2x^{2}-5000x+9000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -5000 ni b va 9000 ni c bilan almashtiring.

$$x=\frac{-\left(-5000\right)±\sqrt{\left(-5000\right)^{2}-4\times 2\times 9000}}{2\times 2}$$

-5000 kvadratini chiqarish.

$$x=\frac{-\left(-5000\right)±\sqrt{25000000-4\times 2\times 9000}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-5000\right)±\sqrt{25000000-8\times 9000}}{2\times 2}$$

-8 ni 9000 marotabaga ko'paytirish.

$$x=\frac{-\left(-5000\right)±\sqrt{25000000-72000}}{2\times 2}$$

25000000 ni -72000 ga qo'shish.

$$x=\frac{-\left(-5000\right)±\sqrt{24928000}}{2\times 2}$$

24928000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5000\right)±80\sqrt{3895}}{2\times 2}$$

-5000 ning teskarisi 5000 ga teng.

$$x=\frac{5000±80\sqrt{3895}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{5000±80\sqrt{3895}}{4}$$

x=\frac{5000±80\sqrt{3895}}{4} tenglamasini yeching, bunda ± musbat. 5000 ni 80\sqrt{3895} ga qo'shish.

$$x=\frac{80\sqrt{3895}+5000}{4}$$

5000+80\sqrt{3895} ni 4 ga bo'lish.

$$x=20\sqrt{3895}+1250$$

x=\frac{5000±80\sqrt{3895}}{4} tenglamasini yeching, bunda ± manfiy. 5000 dan 80\sqrt{3895} ni ayirish.

$$x=\frac{5000-80\sqrt{3895}}{4}$$

5000-80\sqrt{3895} ni 4 ga bo'lish.

$$x=1250-20\sqrt{3895}$$

Tenglama yechildi.

$$x=20\sqrt{3895}+1250 x=1250-20\sqrt{3895}$$

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.

$$2x^{2}-5000x+9000=0$$

Tenglamaning ikkala tarafidan 9000 ni ayirish.

$$2x^{2}-5000x+9000-9000=-9000$$

O‘zidan 9000 ayirilsa 0 qoladi.

$$2x^{2}-5000x=-9000$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-5000x}{2}=-\frac{9000}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{5000}{2}\right)x=-\frac{9000}{2}$$

-5000 ni 2 ga bo'lish.

$$x^{2}-2500x=-\frac{9000}{2}$$

-9000 ni 2 ga bo'lish.

$$x^{2}-2500x=-4500$$

-2500 ni bo‘lish, x shartining koeffitsienti, 2 ga -1250 olish uchun. Keyin, -1250 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2500x+\left(-1250\right)^{2}=-4500+\left(-1250\right)^{2}$$

-1250 kvadratini chiqarish.

$$x^{2}-2500x+1562500=-4500+1562500$$

-4500 ni 1562500 ga qo'shish.

$$x^{2}-2500x+1562500=1558000$$

x^{2}-2500x+1562500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1250\right)^{2}=1558000$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1250\right)^{2}}=\sqrt{1558000}$$

Qisqartirish.

$$x-1250=20\sqrt{3895} x-1250=-20\sqrt{3895}$$

1250 ni tenglamaning ikkala tarafiga qo'shish.

$$x=20\sqrt{3895}+1250 x=1250-20\sqrt{3895}$$