(x-5)^2-c=0 eching

$$( x - 5 ) ^ { 2 } - c = 0$$

c uchun yechish

$$c=\left(x-5\right)^{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-5\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-10x+25-c=0$$

Ikkala tarafdan x^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-10x+25-c=-x^{2}$$

10x ni ikki tarafga qo’shing.

$$25-c=-x^{2}+10x$$

Ikkala tarafdan 25 ni ayirish.

$$-c=-x^{2}+10x-25$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-c}{-1}=-\frac{\left(x-5\right)^{2}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$c=-\frac{\left(x-5\right)^{2}}{-1}$$

-\left(x-5\right)^{2} ni -1 ga bo'lish.

$$c=\left(x-5\right)^{2}$$

x uchun yechish (complex solution)

$$x=-\sqrt{c}+5$$

$$x=\sqrt{c}+5$$

x uchun yechish

$$x=-\sqrt{c}+5$$

$$x=\sqrt{c}+5\text{, }c\geq 0$$