0.0001x^2+x-192=0 eching

$$0.0001 x ^ { 2 } + x - 192 = 0$$

x uchun yechish

$$x=200\sqrt{673}-5000\approx 188,448708429$$

$$x=-200\sqrt{673}-5000\approx -10188,448708429$$

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.

$$0,0001x^{2}+x-192=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 0,0001 ni a, 1 ni b va -192 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\times 0,0001\left(-192\right)}}{2\times 0,0001}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\times 0,0001\left(-192\right)}}{2\times 0,0001}$$

-4 ni 0,0001 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-0,0004\left(-192\right)}}{2\times 0,0001}$$

-0,0004 ni -192 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+0,0768}}{2\times 0,0001}$$

1 ni 0,0768 ga qo'shish.

$$x=\frac{-1±\sqrt{1,0768}}{2\times 0,0001}$$

1,0768 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±\frac{\sqrt{673}}{25}}{2\times 0,0001}$$

2 ni 0,0001 marotabaga ko'paytirish.

$$x=\frac{-1±\frac{\sqrt{673}}{25}}{0,0002}$$

x=\frac{-1±\frac{\sqrt{673}}{25}}{0,0002} tenglamasini yeching, bunda ± musbat. -1 ni \frac{\sqrt{673}}{25} ga qo'shish.

$$x=\frac{\frac{\sqrt{673}}{25}-1}{0,0002}$$

-1+\frac{\sqrt{673}}{25} ni 0,0002 ga bo'lish -1+\frac{\sqrt{673}}{25} ga k'paytirish 0,0002 ga qaytarish.

$$x=200\sqrt{673}-5000$$

x=\frac{-1±\frac{\sqrt{673}}{25}}{0,0002} tenglamasini yeching, bunda ± manfiy. -1 dan \frac{\sqrt{673}}{25} ni ayirish.

$$x=\frac{-\frac{\sqrt{673}}{25}-1}{0,0002}$$

-1-\frac{\sqrt{673}}{25} ni 0,0002 ga bo'lish -1-\frac{\sqrt{673}}{25} ga k'paytirish 0,0002 ga qaytarish.

$$x=-200\sqrt{673}-5000$$

Tenglama yechildi.

$$x=200\sqrt{673}-5000 x=-200\sqrt{673}-5000$$

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.

$$0.0001x^{2}+x-192=0$$

192 ni tenglamaning ikkala tarafiga qo'shish.

$$0.0001x^{2}+x-192-\left(-192\right)=-\left(-192\right)$$

O‘zidan -192 ayirilsa 0 qoladi.

$$0.0001x^{2}+x=-\left(-192\right)$$

0 dan -192 ni ayirish.

$$0.0001x^{2}+x=192$$

Ikkala tarafini 10000 ga ko‘paytiring.

$$\frac{0.0001x^{2}+x}{0.0001}=\frac{192}{0.0001}$$

0.0001 ga bo'lish 0.0001 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{0.0001}x=\frac{192}{0.0001}$$

1 ni 0.0001 ga bo'lish 1 ga k'paytirish 0.0001 ga qaytarish.

$$x^{2}+10000x=\frac{192}{0.0001}$$

192 ni 0.0001 ga bo'lish 192 ga k'paytirish 0.0001 ga qaytarish.

$$x^{2}+10000x=1920000$$

10000 ni bo‘lish, x shartining koeffitsienti, 2 ga 5000 olish uchun. Keyin, 5000 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+10000x+5000^{2}=1920000+5000^{2}$$

5000 kvadratini chiqarish.

$$x^{2}+10000x+25000000=1920000+25000000$$

1920000 ni 25000000 ga qo'shish.

$$x^{2}+10000x+25000000=26920000$$

x^{2}+10000x+25000000 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+5000\right)^{2}=26920000$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5000\right)^{2}}=\sqrt{26920000}$$

Qisqartirish.

$$x+5000=200\sqrt{673} x+5000=-200\sqrt{673}$$

Tenglamaning ikkala tarafidan 5000 ni ayirish.

$$x=200\sqrt{673}-5000 x=-200\sqrt{673}-5000$$