50+x^2-10x=50 eching

$$50 + x ^ { 2 } - 10 x = 50$$

x uchun yechish

$$x=10$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 50 ni ayirish.

$$50+x^{2}-10x-50=0$$

0 olish uchun 50 dan 50 ni ayirish.

$$x^{2}-10x=0$$

x omili.

$$x\left(x-10\right)=0$$

Tenglamani yechish uchun x=0 va x-10=0 ni yeching.

$$x=0 x=10$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-10x+50=50$$

Tenglamaning ikkala tarafidan 50 ni ayirish.

$$x^{2}-10x+50-50=50-50$$

O‘zidan 50 ayirilsa 0 qoladi.

$$x^{2}-10x+50-50=0$$

50 dan 50 ni ayirish.

$$x^{2}-10x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -10 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2}$$

\left(-10\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±10}{2}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±10}{2}$$

x=\frac{10±10}{2} tenglamasini yeching, bunda ± musbat. 10 ni 10 ga qo'shish.

$$x=\frac{20}{2}$$

20 ni 2 ga bo'lish.

$$x=10$$

x=\frac{10±10}{2} tenglamasini yeching, bunda ± manfiy. 10 dan 10 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=10 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 50 ni ayirish.

$$50+x^{2}-10x-50=0$$

0 olish uchun 50 dan 50 ni ayirish.

$$x^{2}-10x=0$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

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

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-5\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-5=5 x-5=-5$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10 x=0$$