x^2-28x=0 eching

$$x ^ { 2 } - 28 x = 0$$

x uchun yechish

$$x=28$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(x-28\right)=0$$

Tenglamani yechish uchun x=0 va x-28=0 ni yeching.

$$x=0 x=28$$

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.

$$x^{2}-28x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -28 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2}$$

\left(-28\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28\right)±28}{2}$$

-28 ning teskarisi 28 ga teng.

$$x=\frac{28±28}{2}$$

x=\frac{28±28}{2} tenglamasini yeching, bunda ± musbat. 28 ni 28 ga qo'shish.

$$x=\frac{56}{2}$$

56 ni 2 ga bo'lish.

$$x=28$$

x=\frac{28±28}{2} tenglamasini yeching, bunda ± manfiy. 28 dan 28 ni ayirish.

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=28 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-28x=0$$

-28 ni bo‘lish, x shartining koeffitsienti, 2 ga -14 olish uchun. Keyin, -14 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-28x+\left(-14\right)^{2}=\left(-14\right)^{2}$$

-14 kvadratini chiqarish.

$$x^{2}-28x+196=196$$

x^{2}-28x+196 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-14\right)^{2}=196$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{196}$$

Qisqartirish.

$$x-14=14 x-14=-14$$

14 ni tenglamaning ikkala tarafiga qo'shish.

$$x=28 x=0$$