6x^2+25=0 eching

$$6 x ^ { 2 } + 25 = 0$$

x uchun yechish (complex solution)

$$x=-\frac{5\sqrt{6}i}{6}\approx -0-2,041241452i$$

$$x=\frac{5\sqrt{6}i}{6}\approx 2,041241452i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 25 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$6x^{2}=-25$$

Ikki tarafini 6 ga bo‘ling.

$$x^{2}=-\frac{25}{6}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{6}i}{6} x=-\frac{5\sqrt{6}i}{6}$$

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.

$$6x^{2}+25=0$$

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 25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 25}}{2\times 6}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 6\times 25}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-24\times 25}}{2\times 6}$$

-24 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-600}}{2\times 6}$$

-600 ning kvadrat ildizini chiqarish.

$$x=\frac{0±10\sqrt{6}i}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{0±10\sqrt{6}i}{12}$$

x=\frac{0±10\sqrt{6}i}{12} tenglamasini yeching, bunda ± musbat.

$$x=\frac{5\sqrt{6}i}{6}$$

x=\frac{0±10\sqrt{6}i}{12} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{5\sqrt{6}i}{6}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{6}i}{6} x=-\frac{5\sqrt{6}i}{6}$$