10x^2-56=88-6x^2 eching

$$10 x ^ { 2 } - 56 = 88 - 6 x ^ { 2 }$$

x uchun yechish

$$x=3$$

$$x=-3$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 88 ni ayirish.

$$10x^{2}-56-88=-6x^{2}$$

-144 olish uchun -56 dan 88 ni ayirish.

$$10x^{2}-144=-6x^{2}$$

6x^{2} ni ikki tarafga qo’shing.

$$10x^{2}-144+6x^{2}=0$$

16x^{2} ni olish uchun 10x^{2} va 6x^{2} ni birlashtirish.

$$16x^{2}-144=0$$

Ikki tarafini 16 ga bo‘ling.

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

Hisoblang: x^{2}-9. x^{2}-9 ni x^{2}-3^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Tenglamani yechish uchun x-3=0 va x+3=0 ni yeching.

$$x=3 x=-3$$

Kvadrat ildizini topish bo'yicha qadamlar

6x^{2} ni ikki tarafga qo’shing.

$$10x^{2}-56+6x^{2}=88$$

16x^{2} ni olish uchun 10x^{2} va 6x^{2} ni birlashtirish.

$$16x^{2}-56=88$$

56 ni ikki tarafga qo’shing.

$$16x^{2}=88+56$$

144 olish uchun 88 va 56'ni qo'shing.

$$16x^{2}=144$$

Ikki tarafini 16 ga bo‘ling.

$$x^{2}=\frac{144}{16}$$

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

$$x^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3 x=-3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 88 ni ayirish.

$$10x^{2}-56-88=-6x^{2}$$

-144 olish uchun -56 dan 88 ni ayirish.

$$10x^{2}-144=-6x^{2}$$

6x^{2} ni ikki tarafga qo’shing.

$$10x^{2}-144+6x^{2}=0$$

16x^{2} ni olish uchun 10x^{2} va 6x^{2} ni birlashtirish.

$$16x^{2}-144=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 16 ni a, 0 ni b va -144 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-144\right)}}{2\times 16}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 16\left(-144\right)}}{2\times 16}$$

-4 ni 16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-64\left(-144\right)}}{2\times 16}$$

-64 ni -144 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{9216}}{2\times 16}$$

9216 ning kvadrat ildizini chiqarish.

$$x=\frac{0±96}{2\times 16}$$

2 ni 16 marotabaga ko'paytirish.

$$x=\frac{0±96}{32}$$

x=\frac{0±96}{32} tenglamasini yeching, bunda ± musbat. 96 ni 32 ga bo'lish.

$$x=3$$

x=\frac{0±96}{32} tenglamasini yeching, bunda ± manfiy. -96 ni 32 ga bo'lish.

$$x=-3$$

Tenglama yechildi.

$$x=3 x=-3$$