(100+4x^2)divx=8x eching

$$(100+4 { x }^{ 2 } ) \div x=8x$$

x uchun yechish

$$x=5$$

$$x=-5$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$100+4x^{2}=8xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$100+4x^{2}=8x^{2}$$

Ikkala tarafdan 8x^{2} ni ayirish.

$$100+4x^{2}-8x^{2}=0$$

-4x^{2} ni olish uchun 4x^{2} va -8x^{2} ni birlashtirish.

$$100-4x^{2}=0$$

Ikkala tarafdan 100 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-4x^{2}=-100$$

Ikki tarafini -4 ga bo‘ling.

$$x^{2}=\frac{-100}{-4}$$

25 ni olish uchun -100 ni -4 ga bo‘ling.

$$x^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=5 x=-5$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

$$100+4x^{2}=8xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$100+4x^{2}=8x^{2}$$

Ikkala tarafdan 8x^{2} ni ayirish.

$$100+4x^{2}-8x^{2}=0$$

-4x^{2} ni olish uchun 4x^{2} va -8x^{2} ni birlashtirish.

$$100-4x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-4x^{2}+100=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 100}}{2\left(-4\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-4\right)\times 100}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16\times 100}}{2\left(-4\right)}$$

16 ni 100 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1600}}{2\left(-4\right)}$$

1600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±40}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±40}{-8}$$

x=\frac{0±40}{-8} tenglamasini yeching, bunda ± musbat. 40 ni -8 ga bo'lish.

$$x=-5$$

x=\frac{0±40}{-8} tenglamasini yeching, bunda ± manfiy. -40 ni -8 ga bo'lish.

$$x=5$$

Tenglama yechildi.

$$x=-5 x=5$$