0=x^2-100x+560000 eching

$$0 = x ^ { 2 } - 100 x + 560000$$

x uchun yechish (complex solution)

$$x=50+50\sqrt{223}i\approx 50+746,659226153i$$

$$x=-50\sqrt{223}i+50\approx 50-746,659226153i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-100x+560000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -100 ni b va 560000 ni c bilan almashtiring.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 560000}}{2}$$

-100 kvadratini chiqarish.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4\times 560000}}{2}$$

-4 ni 560000 marotabaga ko'paytirish.

$$x=\frac{-\left(-100\right)±\sqrt{10000-2240000}}{2}$$

10000 ni -2240000 ga qo'shish.

$$x=\frac{-\left(-100\right)±\sqrt{-2230000}}{2}$$

-2230000 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-100\right)±100\sqrt{223}i}{2}$$

-100 ning teskarisi 100 ga teng.

$$x=\frac{100±100\sqrt{223}i}{2}$$

x=\frac{100±100\sqrt{223}i}{2} tenglamasini yeching, bunda ± musbat. 100 ni 100i\sqrt{223} ga qo'shish.

$$x=\frac{100+100\sqrt{223}i}{2}$$

100+100i\sqrt{223} ni 2 ga bo'lish.

$$x=50+50\sqrt{223}i$$

x=\frac{100±100\sqrt{223}i}{2} tenglamasini yeching, bunda ± manfiy. 100 dan 100i\sqrt{223} ni ayirish.

$$x=\frac{-100\sqrt{223}i+100}{2}$$

100-100i\sqrt{223} ni 2 ga bo'lish.

$$x=-50\sqrt{223}i+50$$

Tenglama yechildi.

$$x=50+50\sqrt{223}i x=-50\sqrt{223}i+50$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-100x+560000=0$$

Ikkala tarafdan 560000 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-100x=-560000$$

-100 ni bo‘lish, x shartining koeffitsienti, 2 ga -50 olish uchun. Keyin, -50 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-100x+\left(-50\right)^{2}=-560000+\left(-50\right)^{2}$$

-50 kvadratini chiqarish.

$$x^{2}-100x+2500=-560000+2500$$

-560000 ni 2500 ga qo'shish.

$$x^{2}-100x+2500=-557500$$

x^{2}-100x+2500 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-50\right)^{2}=-557500$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{-557500}$$

Qisqartirish.

$$x-50=50\sqrt{223}i x-50=-50\sqrt{223}i$$

50 ni tenglamaning ikkala tarafiga qo'shish.

$$x=50+50\sqrt{223}i x=-50\sqrt{223}i+50$$