301+2t^2=300t eching

$$301 + 2 t ^ { 2 } = 300 t$$

t uchun yechish

$$t=\frac{\sqrt{21898}}{2}+75\approx 148,989864171$$

$$t=-\frac{\sqrt{21898}}{2}+75\approx 1,010135829$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 300t ni ayirish.

$$301+2t^{2}-300t=0$$

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.

$$2t^{2}-300t+301=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -300 ni b va 301 ni c bilan almashtiring.

$$t=\frac{-\left(-300\right)±\sqrt{\left(-300\right)^{2}-4\times 2\times 301}}{2\times 2}$$

-300 kvadratini chiqarish.

$$t=\frac{-\left(-300\right)±\sqrt{90000-4\times 2\times 301}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$t=\frac{-\left(-300\right)±\sqrt{90000-8\times 301}}{2\times 2}$$

-8 ni 301 marotabaga ko'paytirish.

$$t=\frac{-\left(-300\right)±\sqrt{90000-2408}}{2\times 2}$$

90000 ni -2408 ga qo'shish.

$$t=\frac{-\left(-300\right)±\sqrt{87592}}{2\times 2}$$

87592 ning kvadrat ildizini chiqarish.

$$t=\frac{-\left(-300\right)±2\sqrt{21898}}{2\times 2}$$

-300 ning teskarisi 300 ga teng.

$$t=\frac{300±2\sqrt{21898}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$t=\frac{300±2\sqrt{21898}}{4}$$

t=\frac{300±2\sqrt{21898}}{4} tenglamasini yeching, bunda ± musbat. 300 ni 2\sqrt{21898} ga qo'shish.

$$t=\frac{2\sqrt{21898}+300}{4}$$

300+2\sqrt{21898} ni 4 ga bo'lish.

$$t=\frac{\sqrt{21898}}{2}+75$$

t=\frac{300±2\sqrt{21898}}{4} tenglamasini yeching, bunda ± manfiy. 300 dan 2\sqrt{21898} ni ayirish.

$$t=\frac{300-2\sqrt{21898}}{4}$$

300-2\sqrt{21898} ni 4 ga bo'lish.

$$t=-\frac{\sqrt{21898}}{2}+75$$

Tenglama yechildi.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 300t ni ayirish.

$$301+2t^{2}-300t=0$$

Ikkala tarafdan 301 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2t^{2}-300t=-301$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2t^{2}-300t}{2}=-\frac{301}{2}$$

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

$$t^{2}+\left(-\frac{300}{2}\right)t=-\frac{301}{2}$$

-300 ni 2 ga bo'lish.

$$t^{2}-150t=-\frac{301}{2}$$

-150 ni bo‘lish, x shartining koeffitsienti, 2 ga -75 olish uchun. Keyin, -75 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$t^{2}-150t+\left(-75\right)^{2}=-\frac{301}{2}+\left(-75\right)^{2}$$

-75 kvadratini chiqarish.

$$t^{2}-150t+5625=-\frac{301}{2}+5625$$

-\frac{301}{2} ni 5625 ga qo'shish.

$$t^{2}-150t+5625=\frac{10949}{2}$$

t^{2}-150t+5625 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(t-75\right)^{2}=\frac{10949}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(t-75\right)^{2}}=\sqrt{\frac{10949}{2}}$$

Qisqartirish.

$$t-75=\frac{\sqrt{21898}}{2} t-75=-\frac{\sqrt{21898}}{2}$$

75 ni tenglamaning ikkala tarafiga qo'shish.

$$t=\frac{\sqrt{21898}}{2}+75 t=-\frac{\sqrt{21898}}{2}+75$$