6x^2+150=0 eching

$$6 x ^ { 2 } + 150 = 0$$

x uchun yechish (complex solution)

$$x=-5i$$

$$x=5i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 150 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$6x^{2}=-150$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=\frac{-150}{6}$$

-25 ni olish uchun -150 ni 6 ga bo‘ling.

$$x^{2}=-25$$

Tenglama yechildi.

$$x=5i x=-5i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$6x^{2}+150=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 0 ni b va 150 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 150}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\times 150}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\times 150}}{2\times 6}$$

-24 ni 150 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-3600}}{2\times 6}$$

-3600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±60i}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±60i}{12}$$

x=\frac{0±60i}{12} tenglamasini yeching, bunda ± musbat.

$$x=5i$$

x=\frac{0±60i}{12} tenglamasini yeching, bunda ± manfiy.

$$x=-5i$$

Tenglama yechildi.

$$x=5i x=-5i$$