9x^2+25=0 eching

$$9 { x }^{ 2 } +25 = 0$$

x uchun yechish (complex solution)

$$x=-\frac{5}{3}i\approx -1,666666667i$$

$$x=\frac{5}{3}i\approx 1,666666667i$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$9x^{2}=-25$$

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=-\frac{25}{9}$$

Tenglama yechildi.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$

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.

$$9x^{2}+25=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 0 ni b va 25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\times 25}}{2\times 9}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 9\times 25}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-36\times 25}}{2\times 9}$$

-36 ni 25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-900}}{2\times 9}$$

-900 ning kvadrat ildizini chiqarish.

$$x=\frac{0±30i}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±30i}{18}$$

x=\frac{0±30i}{18} tenglamasini yeching, bunda ± musbat.

$$x=\frac{5}{3}i$$

x=\frac{0±30i}{18} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{5}{3}i$$

Tenglama yechildi.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$