5x^2-20x=0 eching

$$5 { x }^{ 2 } -20x=0$$

x uchun yechish

$$x=4$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(5x-20\right)=0$$

Tenglamani yechish uchun x=0 va 5x-20=0 ni yeching.

$$x=0 x=4$$

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.

$$5x^{2}-20x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -20 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 5}$$

\left(-20\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±20}{2\times 5}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±20}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{20±20}{10}$$

x=\frac{20±20}{10} tenglamasini yeching, bunda ± musbat. 20 ni 20 ga qo'shish.

$$x=\frac{40}{10}$$

40 ni 10 ga bo'lish.

$$x=4$$

x=\frac{20±20}{10} tenglamasini yeching, bunda ± manfiy. 20 dan 20 ni ayirish.

$$x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=4 x=0$$

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.

$$5x^{2}-20x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-20x}{5}=\frac{0}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{20}{5}\right)x=\frac{0}{5}$$

-20 ni 5 ga bo'lish.

$$x^{2}-4x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}-4x=0$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-4x+\left(-2\right)^{2}=\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=4$$

x^{2}-4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-2\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{4}$$

Qisqartirish.

$$x-2=2 x-2=-2$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=0$$