x^2=left(6-xright)^2+9 eching

$${ x }^{ 2 } = { \left(6-x \right) }^{ 2 } +9$$

x uchun yechish

$$x = \frac{15}{4} = 3\frac{3}{4} = 3,75$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(6-x\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}=36-12x+x^{2}+9$$

45 olish uchun 36 va 9'ni qo'shing.

$$x^{2}=45-12x+x^{2}$$

12x ni ikki tarafga qo’shing.

$$x^{2}+12x=45+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+12x-x^{2}=45$$

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

$$12x=45$$

Ikki tarafini 12 ga bo‘ling.

$$x=\frac{45}{12}$$

\frac{45}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{15}{4}$$