x-98x^2/40000=0 eching

$$x - \frac { 98 x ^ { 2 } } { 40000 } = 0$$

x uchun yechish

$$x = \frac{20000}{49} = 408\frac{8}{49} \approx 408,163265306$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 40000 ga ko'paytirish.

$$40000x-98x^{2}=0$$

x omili.

$$x\left(40000-98x\right)=0$$

Tenglamani yechish uchun x=0 va 40000-98x=0 ni yeching.

$$x=0 x=\frac{20000}{49}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 40000 ga ko'paytirish.

$$40000x-98x^{2}=0$$

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.

$$-98x^{2}+40000x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -98 ni a, 40000 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-40000±\sqrt{40000^{2}}}{2\left(-98\right)}$$

40000^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-40000±40000}{2\left(-98\right)}$$

2 ni -98 marotabaga ko'paytirish.

$$x=\frac{-40000±40000}{-196}$$

x=\frac{-40000±40000}{-196} tenglamasini yeching, bunda ± musbat. -40000 ni 40000 ga qo'shish.

$$x=\frac{0}{-196}$$

0 ni -196 ga bo'lish.

$$x=0$$

x=\frac{-40000±40000}{-196} tenglamasini yeching, bunda ± manfiy. -40000 dan 40000 ni ayirish.

$$x=-\frac{80000}{-196}$$

\frac{-80000}{-196} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{20000}{49}$$

Tenglama yechildi.

$$x=0 x=\frac{20000}{49}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 40000 ga ko'paytirish.

$$40000x-98x^{2}=0$$

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

$$-98x^{2}+40000x=0$$

Ikki tarafini -98 ga bo‘ling.

$$\frac{-98x^{2}+40000x}{-98}=\frac{0}{-98}$$

-98 ga bo'lish -98 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{40000}{-98}x=\frac{0}{-98}$$

\frac{40000}{-98} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{20000}{49}x=\frac{0}{-98}$$

0 ni -98 ga bo'lish.

$$x^{2}-\frac{20000}{49}x=0$$

-\frac{20000}{49} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{10000}{49} olish uchun. Keyin, -\frac{10000}{49} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{20000}{49}x+\left(-\frac{10000}{49}\right)^{2}=\left(-\frac{10000}{49}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{10000}{49} kvadratini chiqarish.

$$x^{2}-\frac{20000}{49}x+\frac{100000000}{2401}=\frac{100000000}{2401}$$

x^{2}-\frac{20000}{49}x+\frac{100000000}{2401} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{10000}{49}\right)^{2}=\frac{100000000}{2401}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{10000}{49}\right)^{2}}=\sqrt{\frac{100000000}{2401}}$$

Qisqartirish.

$$x-\frac{10000}{49}=\frac{10000}{49} x-\frac{10000}{49}=-\frac{10000}{49}$$

\frac{10000}{49} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{20000}{49} x=0$$