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.

$$x=\frac{-20±\sqrt{20^{2}}}{2\times 5}$$

20^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-20±20}{2\times 5}$$

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.

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

0 ni 10 ga bo'lish.

$$x=0$$

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

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

-40 ni 10 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=0 x=-4$$

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.

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

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.

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

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.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=0 x=-4$$