2x^2-10x+25=2x+25 eching

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

x uchun yechish

$$x=6$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 2x ni ayirish.

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

-12x ni olish uchun -10x va -2x ni birlashtirish.

$$2x^{2}-12x+25=25$$

Ikkala tarafdan 25 ni ayirish.

$$2x^{2}-12x+25-25=0$$

0 olish uchun 25 dan 25 ni ayirish.

$$2x^{2}-12x=0$$

x omili.

$$x\left(2x-12\right)=0$$

Tenglamani yechish uchun x=0 va 2x-12=0 ni yeching.

$$x=0 x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

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

-12x ni olish uchun -10x va -2x ni birlashtirish.

$$2x^{2}-12x+25=25$$

Ikkala tarafdan 25 ni ayirish.

$$2x^{2}-12x+25-25=0$$

0 olish uchun 25 dan 25 ni ayirish.

$$2x^{2}-12x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -12 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 2}$$

\left(-12\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±12}{2\times 2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±12}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{12±12}{4}$$

x=\frac{12±12}{4} tenglamasini yeching, bunda ± musbat. 12 ni 12 ga qo'shish.

$$x=\frac{24}{4}$$

24 ni 4 ga bo'lish.

$$x=6$$

x=\frac{12±12}{4} tenglamasini yeching, bunda ± manfiy. 12 dan 12 ni ayirish.

$$x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=6 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

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

-12x ni olish uchun -10x va -2x ni birlashtirish.

$$2x^{2}-12x+25=25$$

Ikkala tarafdan 25 ni ayirish.

$$2x^{2}-12x=25-25$$

0 olish uchun 25 dan 25 ni ayirish.

$$2x^{2}-12x=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-12x}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{2}\right)x=\frac{0}{2}$$

-12 ni 2 ga bo'lish.

$$x^{2}-6x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x^{2}-6x=0$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=9$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x-3=3 x-3=-3$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=6 x=0$$