(x+2)^2=x*(x+49)+9 eching

$$( x + 2 ) ^ { 2 } = x \cdot ( x + 49 ) + 9$$

x uchun yechish

$$x=-\frac{1}{9}\approx -0,111111111$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+2\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+4x+4=x\left(x+49\right)+9$$

x ga x+49 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+4x+4=x^{2}+49x+9$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+4x+4-x^{2}=49x+9$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$4x+4=49x+9$$

Ikkala tarafdan 49x ni ayirish.

$$4x+4-49x=9$$

-45x ni olish uchun 4x va -49x ni birlashtirish.

$$-45x+4=9$$

Ikkala tarafdan 4 ni ayirish.

$$-45x=9-4$$

5 olish uchun 9 dan 4 ni ayirish.

$$-45x=5$$

Ikki tarafini -45 ga bo‘ling.

$$x=\frac{5}{-45}$$

\frac{5}{-45} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{9}$$