36+x^2=(x+24)^2 eching

$$36 + x ^ { 2 } = ( x + 24 ) ^ { 2 }$$

x uchun yechish

$$x = -\frac{45}{4} = -11\frac{1}{4} = -11,25$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+24\right)^{2} kengaytirilishi uchun ishlating.

$$36+x^{2}=x^{2}+48x+576$$

Ikkala tarafdan x^{2} ni ayirish.

$$36+x^{2}-x^{2}=48x+576$$

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

$$36=48x+576$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$48x+576=36$$

Ikkala tarafdan 576 ni ayirish.

$$48x=36-576$$

-540 olish uchun 36 dan 576 ni ayirish.

$$48x=-540$$

Ikki tarafini 48 ga bo‘ling.

$$x=\frac{-540}{48}$$

\frac{-540}{48} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{45}{4}$$