-9x^2+144=0 eching

$$-9 { x }^{ 2 } +144=0$$

x uchun yechish

$$x=4$$

$$x=-4$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 144 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-9x^{2}=-144$$

Ikki tarafini -9 ga bo‘ling.

$$x^{2}=\frac{-144}{-9}$$

16 ni olish uchun -144 ni -9 ga bo‘ling.

$$x^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4 x=-4$$

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.

$$-9x^{2}+144=0$$

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 144 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 144}}{2\left(-9\right)}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{36\times 144}}{2\left(-9\right)}$$

36 ni 144 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{5184}}{2\left(-9\right)}$$

5184 ning kvadrat ildizini chiqarish.

$$x=\frac{0±72}{2\left(-9\right)}$$

2 ni -9 marotabaga ko'paytirish.

$$x=\frac{0±72}{-18}$$

x=\frac{0±72}{-18} tenglamasini yeching, bunda ± musbat. 72 ni -18 ga bo'lish.

$$x=-4$$

x=\frac{0±72}{-18} tenglamasini yeching, bunda ± manfiy. -72 ni -18 ga bo'lish.

$$x=4$$

Tenglama yechildi.

$$x=-4 x=4$$