100x^2+8x+6*3^2=5833 eching

$$100 x ^ { 2 } + 8 x + 6 \cdot 3 ^ { 2 } = 5833$$

x uchun yechish

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25}\approx 7,562078663$$

$$x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}\approx -7,642078663$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$100x^{2}+8x+6\times 9=5833$$

54 hosil qilish uchun 6 va 9 ni ko'paytirish.

$$100x^{2}+8x+54=5833$$

Ikkala tarafdan 5833 ni ayirish.

$$100x^{2}+8x+54-5833=0$$

-5779 olish uchun 54 dan 5833 ni ayirish.

$$100x^{2}+8x-5779=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 100 ni a, 8 ni b va -5779 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\times 100\left(-5779\right)}}{2\times 100}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\times 100\left(-5779\right)}}{2\times 100}$$

-4 ni 100 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64-400\left(-5779\right)}}{2\times 100}$$

-400 ni -5779 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+2311600}}{2\times 100}$$

64 ni 2311600 ga qo'shish.

$$x=\frac{-8±\sqrt{2311664}}{2\times 100}$$

2311664 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±4\sqrt{144479}}{2\times 100}$$

2 ni 100 marotabaga ko'paytirish.

$$x=\frac{-8±4\sqrt{144479}}{200}$$

x=\frac{-8±4\sqrt{144479}}{200} tenglamasini yeching, bunda ± musbat. -8 ni 4\sqrt{144479} ga qo'shish.

$$x=\frac{4\sqrt{144479}-8}{200}$$

-8+4\sqrt{144479} ni 200 ga bo'lish.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

x=\frac{-8±4\sqrt{144479}}{200} tenglamasini yeching, bunda ± manfiy. -8 dan 4\sqrt{144479} ni ayirish.

$$x=\frac{-4\sqrt{144479}-8}{200}$$

-8-4\sqrt{144479} ni 200 ga bo'lish.

$$x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

Tenglama yechildi.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25} x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$100x^{2}+8x+6\times 9=5833$$

54 hosil qilish uchun 6 va 9 ni ko'paytirish.

$$100x^{2}+8x+54=5833$$

Ikkala tarafdan 54 ni ayirish.

$$100x^{2}+8x=5833-54$$

5779 olish uchun 5833 dan 54 ni ayirish.

$$100x^{2}+8x=5779$$

Ikki tarafini 100 ga bo‘ling.

$$\frac{100x^{2}+8x}{100}=\frac{5779}{100}$$

100 ga bo'lish 100 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{8}{100}x=\frac{5779}{100}$$

\frac{8}{100} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{2}{25}x=\frac{5779}{100}$$

\frac{2}{25} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{25} olish uchun. Keyin, \frac{1}{25} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{2}{25}x+\left(\frac{1}{25}\right)^{2}=\frac{5779}{100}+\left(\frac{1}{25}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{25} kvadratini chiqarish.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=\frac{5779}{100}+\frac{1}{625}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5779}{100} ni \frac{1}{625} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{2}{25}x+\frac{1}{625}=\frac{144479}{2500}$$

x^{2}+\frac{2}{25}x+\frac{1}{625} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{25}\right)^{2}=\frac{144479}{2500}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{25}\right)^{2}}=\sqrt{\frac{144479}{2500}}$$

Qisqartirish.

$$x+\frac{1}{25}=\frac{\sqrt{144479}}{50} x+\frac{1}{25}=-\frac{\sqrt{144479}}{50}$$

Tenglamaning ikkala tarafidan \frac{1}{25} ni ayirish.

$$x=\frac{\sqrt{144479}}{50}-\frac{1}{25} x=-\frac{\sqrt{144479}}{50}-\frac{1}{25}$$