6x^2/25=12x^2/25-48x/5+48 eching

$$\frac{ 6 { x }^{ 2 } }{ 25 } = \frac{ 12 { x }^{ 2 } }{ 25 } - \frac{ 48x }{ 5 } +48$$

x uchun yechish

$$x=10\sqrt{2}+20\approx 34,142135624$$

$$x=20-10\sqrt{2}\approx 5,857864376$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 25 ga, 25,5 ning eng kichik karralisiga ko‘paytiring.

$$6x^{2}=12x^{2}-5\times 48x+1200$$

-240 hosil qilish uchun -5 va 48 ni ko'paytirish.

$$6x^{2}=12x^{2}-240x+1200$$

Ikkala tarafdan 12x^{2} ni ayirish.

$$6x^{2}-12x^{2}=-240x+1200$$

-6x^{2} ni olish uchun 6x^{2} va -12x^{2} ni birlashtirish.

$$-6x^{2}=-240x+1200$$

240x ni ikki tarafga qo’shing.

$$-6x^{2}+240x=1200$$

Ikkala tarafdan 1200 ni ayirish.

$$-6x^{2}+240x-1200=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -6 ni a, 240 ni b va -1200 ni c bilan almashtiring.

$$x=\frac{-240±\sqrt{240^{2}-4\left(-6\right)\left(-1200\right)}}{2\left(-6\right)}$$

240 kvadratini chiqarish.

$$x=\frac{-240±\sqrt{57600-4\left(-6\right)\left(-1200\right)}}{2\left(-6\right)}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-240±\sqrt{57600+24\left(-1200\right)}}{2\left(-6\right)}$$

24 ni -1200 marotabaga ko'paytirish.

$$x=\frac{-240±\sqrt{57600-28800}}{2\left(-6\right)}$$

57600 ni -28800 ga qo'shish.

$$x=\frac{-240±\sqrt{28800}}{2\left(-6\right)}$$

28800 ning kvadrat ildizini chiqarish.

$$x=\frac{-240±120\sqrt{2}}{2\left(-6\right)}$$

2 ni -6 marotabaga ko'paytirish.

$$x=\frac{-240±120\sqrt{2}}{-12}$$

x=\frac{-240±120\sqrt{2}}{-12} tenglamasini yeching, bunda ± musbat. -240 ni 120\sqrt{2} ga qo'shish.

$$x=\frac{120\sqrt{2}-240}{-12}$$

-240+120\sqrt{2} ni -12 ga bo'lish.

$$x=20-10\sqrt{2}$$

x=\frac{-240±120\sqrt{2}}{-12} tenglamasini yeching, bunda ± manfiy. -240 dan 120\sqrt{2} ni ayirish.

$$x=\frac{-120\sqrt{2}-240}{-12}$$

-240-120\sqrt{2} ni -12 ga bo'lish.

$$x=10\sqrt{2}+20$$

Tenglama yechildi.

$$x=20-10\sqrt{2} x=10\sqrt{2}+20$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 25 ga, 25,5 ning eng kichik karralisiga ko‘paytiring.

$$6x^{2}=12x^{2}-5\times 48x+1200$$

-240 hosil qilish uchun -5 va 48 ni ko'paytirish.

$$6x^{2}=12x^{2}-240x+1200$$

Ikkala tarafdan 12x^{2} ni ayirish.

$$6x^{2}-12x^{2}=-240x+1200$$

-6x^{2} ni olish uchun 6x^{2} va -12x^{2} ni birlashtirish.

$$-6x^{2}=-240x+1200$$

240x ni ikki tarafga qo’shing.

$$-6x^{2}+240x=1200$$

Ikki tarafini -6 ga bo‘ling.

$$\frac{-6x^{2}+240x}{-6}=\frac{1200}{-6}$$

-6 ga bo'lish -6 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{240}{-6}x=\frac{1200}{-6}$$

240 ni -6 ga bo'lish.

$$x^{2}-40x=\frac{1200}{-6}$$

1200 ni -6 ga bo'lish.

$$x^{2}-40x=-200$$

-40 ni bo‘lish, x shartining koeffitsienti, 2 ga -20 olish uchun. Keyin, -20 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-40x+\left(-20\right)^{2}=-200+\left(-20\right)^{2}$$

-20 kvadratini chiqarish.

$$x^{2}-40x+400=-200+400$$

-200 ni 400 ga qo'shish.

$$x^{2}-40x+400=200$$

x^{2}-40x+400 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-20\right)^{2}=200$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-20\right)^{2}}=\sqrt{200}$$

Qisqartirish.

$$x-20=10\sqrt{2} x-20=-10\sqrt{2}$$

20 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10\sqrt{2}+20 x=20-10\sqrt{2}$$