1000+x^2=500 eching

$$1000 + x ^ { 2 } = 500$$

x uchun yechish (complex solution)

$$x=-10\sqrt{5}i\approx -0-22,360679775i$$

$$x=10\sqrt{5}i\approx 22,360679775i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 1000 ni ayirish.

$$x^{2}=500-1000$$

-500 olish uchun 500 dan 1000 ni ayirish.

$$x^{2}=-500$$

Tenglama yechildi.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 500 ni ayirish.

$$1000+x^{2}-500=0$$

500 olish uchun 1000 dan 500 ni ayirish.

$$500+x^{2}=0$$

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.

$$x^{2}+500=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va 500 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 500}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 500}}{2}$$

-4 ni 500 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-2000}}{2}$$

-2000 ning kvadrat ildizini chiqarish.

$$x=\frac{0±20\sqrt{5}i}{2}$$

x=\frac{0±20\sqrt{5}i}{2} tenglamasini yeching, bunda ± musbat.

$$x=10\sqrt{5}i$$

x=\frac{0±20\sqrt{5}i}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-10\sqrt{5}i$$

Tenglama yechildi.

$$x=10\sqrt{5}i x=-10\sqrt{5}i$$