2x^2-50x=0 eching

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

x uchun yechish

$$x=25$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(2x-50\right)=0$$

Tenglamani yechish uchun x=0 va 2x-50=0 ni yeching.

$$x=0 x=25$$

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -50 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}}}{2\times 2}$$

\left(-50\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-50\right)±50}{2\times 2}$$

-50 ning teskarisi 50 ga teng.

$$x=\frac{50±50}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{50±50}{4}$$

x=\frac{50±50}{4} tenglamasini yeching, bunda ± musbat. 50 ni 50 ga qo'shish.

$$x=\frac{100}{4}$$

100 ni 4 ga bo'lish.

$$x=25$$

x=\frac{50±50}{4} tenglamasini yeching, bunda ± manfiy. 50 dan 50 ni ayirish.

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

0 ni 4 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=25 x=0$$

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.

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

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-50x}{2}=\frac{0}{2}$$

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

$$x^{2}+\left(-\frac{50}{2}\right)x=\frac{0}{2}$$

-50 ni 2 ga bo'lish.

$$x^{2}-25x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

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

-25 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{25}{2} olish uchun. Keyin, -\frac{25}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{25}{2} kvadratini chiqarish.

$$x^{2}-25x+\frac{625}{4}=\frac{625}{4}$$

x^{2}-25x+\frac{625}{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.

$$\left(x-\frac{25}{2}\right)^{2}=\frac{625}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{25}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Qisqartirish.

$$x-\frac{25}{2}=\frac{25}{2} x-\frac{25}{2}=-\frac{25}{2}$$

\frac{25}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=25 x=0$$