1/2*30*(253^2-x^2)=-30*155 eching

$$\frac{ 1 }{ 2 } \times 30 \times ( { 253 }^{ 2 } - { x }^{ 2 } )=-30 \times 155$$

x uchun yechish

$$x=\sqrt{64319}\approx 253,611908238$$

$$x=-\sqrt{64319}\approx -253,611908238$$

Kvadrat ildizini topish bo'yicha qadamlar

15 hosil qilish uchun \frac{1}{2} va 30 ni ko'paytirish.

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

2 daraja ko‘rsatkichini 253 ga hisoblang va 64009 ni qiymatni oling.

$$15\left(64009-x^{2}\right)=-30\times 155$$

15 ga 64009-x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$960135-15x^{2}=-30\times 155$$

-4650 hosil qilish uchun -30 va 155 ni ko'paytirish.

$$960135-15x^{2}=-4650$$

Ikkala tarafdan 960135 ni ayirish.

$$-15x^{2}=-4650-960135$$

-964785 olish uchun -4650 dan 960135 ni ayirish.

$$-15x^{2}=-964785$$

Ikki tarafini -15 ga bo‘ling.

$$x^{2}=\frac{-964785}{-15}$$

64319 ni olish uchun -964785 ni -15 ga bo‘ling.

$$x^{2}=64319$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{64319} x=-\sqrt{64319}$$

Kvadrat tenglamalaridan foydalanish qoidalari

15 hosil qilish uchun \frac{1}{2} va 30 ni ko'paytirish.

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

2 daraja ko‘rsatkichini 253 ga hisoblang va 64009 ni qiymatni oling.

$$15\left(64009-x^{2}\right)=-30\times 155$$

15 ga 64009-x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$960135-15x^{2}=-30\times 155$$

-4650 hosil qilish uchun -30 va 155 ni ko'paytirish.

$$960135-15x^{2}=-4650$$

4650 ni ikki tarafga qo’shing.

$$960135-15x^{2}+4650=0$$

964785 olish uchun 960135 va 4650'ni qo'shing.

$$964785-15x^{2}=0$$

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.

$$-15x^{2}+964785=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -15 ni a, 0 ni b va 964785 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

-4 ni -15 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{60\times 964785}}{2\left(-15\right)}$$

60 ni 964785 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{57887100}}{2\left(-15\right)}$$

57887100 ning kvadrat ildizini chiqarish.

$$x=\frac{0±30\sqrt{64319}}{2\left(-15\right)}$$

2 ni -15 marotabaga ko'paytirish.

$$x=\frac{0±30\sqrt{64319}}{-30}$$

x=\frac{0±30\sqrt{64319}}{-30} tenglamasini yeching, bunda ± musbat.

$$x=-\sqrt{64319}$$

x=\frac{0±30\sqrt{64319}}{-30} tenglamasini yeching, bunda ± manfiy.

$$x=\sqrt{64319}$$

Tenglama yechildi.

$$x=-\sqrt{64319} x=\sqrt{64319}$$