x^2-13x^2+40=0 eching

$${ x }^{ 2 } -13 { x }^{ 2 } +40=0$$

x uchun yechish

$$x = \frac{\sqrt{30}}{3} \approx 1,825741858$$

$$x = -\frac{\sqrt{30}}{3} \approx -1,825741858$$

Kvadrat ildizini topish bo'yicha qadamlar

-12x^{2} ni olish uchun x^{2} va -13x^{2} ni birlashtirish.

$$-12x^{2}+40=0$$

Ikkala tarafdan 40 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-12x^{2}=-40$$

Ikki tarafini -12 ga bo‘ling.

$$x^{2}=\frac{-40}{-12}$$

\frac{-40}{-12} ulushini -4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{10}{3}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-12x^{2} ni olish uchun x^{2} va -13x^{2} ni birlashtirish.

$$-12x^{2}+40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -12 ni a, 0 ni b va 40 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

-4 ni -12 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{48\times 40}}{2\left(-12\right)}$$

48 ni 40 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1920}}{2\left(-12\right)}$$

1920 ning kvadrat ildizini chiqarish.

$$x=\frac{0±8\sqrt{30}}{2\left(-12\right)}$$

2 ni -12 marotabaga ko'paytirish.

$$x=\frac{0±8\sqrt{30}}{-24}$$

x=\frac{0±8\sqrt{30}}{-24} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{\sqrt{30}}{3}$$

x=\frac{0±8\sqrt{30}}{-24} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{\sqrt{30}}{3}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{30}}{3} x=\frac{\sqrt{30}}{3}$$