800x^2-60000x=0 eching

$$800 x ^ { 2 } - 60000 x = 0$$

x uchun yechish

$$x=75$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(800x-60000\right)=0$$

Tenglamani yechish uchun x=0 va 800x-60000=0 ni yeching.

$$x=0 x=75$$

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.

$$800x^{2}-60000x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 800 ni a, -60000 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-60000\right)±\sqrt{\left(-60000\right)^{2}}}{2\times 800}$$

\left(-60000\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-60000\right)±60000}{2\times 800}$$

-60000 ning teskarisi 60000 ga teng.

$$x=\frac{60000±60000}{2\times 800}$$

2 ni 800 marotabaga ko'paytirish.

$$x=\frac{60000±60000}{1600}$$

x=\frac{60000±60000}{1600} tenglamasini yeching, bunda ± musbat. 60000 ni 60000 ga qo'shish.

$$x=\frac{120000}{1600}$$

120000 ni 1600 ga bo'lish.

$$x=75$$

x=\frac{60000±60000}{1600} tenglamasini yeching, bunda ± manfiy. 60000 dan 60000 ni ayirish.

$$x=\frac{0}{1600}$$

0 ni 1600 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=75 x=0$$

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.

$$800x^{2}-60000x=0$$

Ikki tarafini 800 ga bo‘ling.

$$\frac{800x^{2}-60000x}{800}=\frac{0}{800}$$

800 ga bo'lish 800 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{60000}{800}\right)x=\frac{0}{800}$$

-60000 ni 800 ga bo'lish.

$$x^{2}-75x=\frac{0}{800}$$

0 ni 800 ga bo'lish.

$$x^{2}-75x=0$$

-75 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{75}{2} olish uchun. Keyin, -\frac{75}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-75x+\left(-\frac{75}{2}\right)^{2}=\left(-\frac{75}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{75}{2} kvadratini chiqarish.

$$x^{2}-75x+\frac{5625}{4}=\frac{5625}{4}$$

x^{2}-75x+\frac{5625}{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.

$$\left(x-\frac{75}{2}\right)^{2}=\frac{5625}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{75}{2}\right)^{2}}=\sqrt{\frac{5625}{4}}$$

Qisqartirish.

$$x-\frac{75}{2}=\frac{75}{2} x-\frac{75}{2}=-\frac{75}{2}$$

\frac{75}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=75 x=0$$