52-9x^2=24 eching

$$52 - 9 x ^ { 2 } = 24$$

x uchun yechish

$$x = \frac{2 \sqrt{7}}{3} \approx 1,763834207$$

$$x = -\frac{2 \sqrt{7}}{3} \approx -1,763834207$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 52 ni ayirish.

$$-9x^{2}=24-52$$

-28 olish uchun 24 dan 52 ni ayirish.

$$-9x^{2}=-28$$

Ikki tarafini -9 ga bo‘ling.

$$x^{2}=\frac{-28}{-9}$$

Ikkala surat va maxrajdan manfiy belgini olib tashlash bilan \frac{-28}{-9} kasrini \frac{28}{9} ga soddalashtirish mumkin.

$$x^{2}=\frac{28}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{7}}{3} x=-\frac{2\sqrt{7}}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 24 ni ayirish.

$$52-9x^{2}-24=0$$

28 olish uchun 52 dan 24 ni ayirish.

$$28-9x^{2}=0$$

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.

$$-9x^{2}+28=0$$

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 28 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 28}}{2\left(-9\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 28}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{36\times 28}}{2\left(-9\right)}$$

36 ni 28 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1008}}{2\left(-9\right)}$$

1008 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{7}}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{7}}{-18}$$

x=\frac{0±12\sqrt{7}}{-18} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{2\sqrt{7}}{3}$$

x=\frac{0±12\sqrt{7}}{-18} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{2\sqrt{7}}{3}$$

Tenglama yechildi.

$$x=-\frac{2\sqrt{7}}{3} x=\frac{2\sqrt{7}}{3}$$