-x^2+20=0 eching

$$- x ^ { 2 } + 20 = 0$$

x uchun yechish

$$x=2\sqrt{5}\approx 4,472135955$$

$$x=-2\sqrt{5}\approx -4,472135955$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 20 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-x^{2}=-20$$

Ikki tarafini -1 ga bo‘ling.

$$x^{2}=\frac{-20}{-1}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-20}{-1} kasrini 20 ga soddalashtirish mumkin.

$$x^{2}=20$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{5} x=-2\sqrt{5}$$

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.

$$-x^{2}+20=0$$

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 20 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 20}}{2\left(-1\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 20}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{4\times 20}}{2\left(-1\right)}$$

4 ni 20 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{80}}{2\left(-1\right)}$$

80 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{5}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{5}}{-2}$$

x=\frac{0±4\sqrt{5}}{-2} tenglamasini yeching, bunda ± musbat.

$$x=-2\sqrt{5}$$

x=\frac{0±4\sqrt{5}}{-2} tenglamasini yeching, bunda ± manfiy.

$$x=2\sqrt{5}$$

Tenglama yechildi.

$$x=-2\sqrt{5} x=2\sqrt{5}$$