14-9a^2=-16-4a^2 eching

$$14 - 9 a ^ { 2 } = - 16 - 4 a ^ { 2 }$$

a uchun yechish

$$a=\sqrt{6}\approx 2,449489743$$

$$a=-\sqrt{6}\approx -2,449489743$$

Kvadrat ildizini topish bo'yicha qadamlar

4a^{2} ni ikki tarafga qo’shing.

$$14-9a^{2}+4a^{2}=-16$$

-5a^{2} ni olish uchun -9a^{2} va 4a^{2} ni birlashtirish.

$$14-5a^{2}=-16$$

Ikkala tarafdan 14 ni ayirish.

$$-5a^{2}=-16-14$$

-30 olish uchun -16 dan 14 ni ayirish.

$$-5a^{2}=-30$$

Ikki tarafini -5 ga bo‘ling.

$$a^{2}=\frac{-30}{-5}$$

6 ni olish uchun -30 ni -5 ga bo‘ling.

$$a^{2}=6$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$a=\sqrt{6} a=-\sqrt{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan -16 ni ayirish.

$$14-9a^{2}-\left(-16\right)=-4a^{2}$$

-16 ning teskarisi 16 ga teng.

$$14-9a^{2}+16=-4a^{2}$$

4a^{2} ni ikki tarafga qo’shing.

$$14-9a^{2}+16+4a^{2}=0$$

30 olish uchun 14 va 16'ni qo'shing.

$$30-9a^{2}+4a^{2}=0$$

-5a^{2} ni olish uchun -9a^{2} va 4a^{2} ni birlashtirish.

$$30-5a^{2}=0$$

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.

$$-5a^{2}+30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, 0 ni b va 30 ni c bilan almashtiring.

$$a=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

0 kvadratini chiqarish.

$$a=\frac{0±\sqrt{-4\left(-5\right)\times 30}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{20\times 30}}{2\left(-5\right)}$$

20 ni 30 marotabaga ko'paytirish.

$$a=\frac{0±\sqrt{600}}{2\left(-5\right)}$$

600 ning kvadrat ildizini chiqarish.

$$a=\frac{0±10\sqrt{6}}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$a=\frac{0±10\sqrt{6}}{-10}$$

a=\frac{0±10\sqrt{6}}{-10} tenglamasini yeching, bunda ± musbat.

$$a=-\sqrt{6}$$

a=\frac{0±10\sqrt{6}}{-10} tenglamasini yeching, bunda ± manfiy.

$$a=\sqrt{6}$$

Tenglama yechildi.

$$a=-\sqrt{6} a=\sqrt{6}$$