x^2-20x+570=0 eching

$${ x }^{ 2 } -20x+570=0$$

x uchun yechish (complex solution)

$$x=10+\sqrt{470}i\approx 10+21,679483389i$$

$$x=-\sqrt{470}i+10\approx 10-21,679483389i$$

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.

$$x^{2}-20x+570=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -20 ni b va 570 ni c bilan almashtiring.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 570}}{2}$$

-20 kvadratini chiqarish.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 570}}{2}$$

-4 ni 570 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400-2280}}{2}$$

400 ni -2280 ga qo'shish.

$$x=\frac{-\left(-20\right)±\sqrt{-1880}}{2}$$

-1880 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±2\sqrt{470}i}{2}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±2\sqrt{470}i}{2}$$

x=\frac{20±2\sqrt{470}i}{2} tenglamasini yeching, bunda ± musbat. 20 ni 2i\sqrt{470} ga qo'shish.

$$x=\frac{20+2\sqrt{470}i}{2}$$

20+2i\sqrt{470} ni 2 ga bo'lish.

$$x=10+\sqrt{470}i$$

x=\frac{20±2\sqrt{470}i}{2} tenglamasini yeching, bunda ± manfiy. 20 dan 2i\sqrt{470} ni ayirish.

$$x=\frac{-2\sqrt{470}i+20}{2}$$

20-2i\sqrt{470} ni 2 ga bo'lish.

$$x=-\sqrt{470}i+10$$

Tenglama yechildi.

$$x=10+\sqrt{470}i x=-\sqrt{470}i+10$$

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.

$$x^{2}-20x+570=0$$

Tenglamaning ikkala tarafidan 570 ni ayirish.

$$x^{2}-20x+570-570=-570$$

O‘zidan 570 ayirilsa 0 qoladi.

$$x^{2}-20x=-570$$

-20 ni bo‘lish, x shartining koeffitsienti, 2 ga -10 olish uchun. Keyin, -10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-20x+\left(-10\right)^{2}=-570+\left(-10\right)^{2}$$

-10 kvadratini chiqarish.

$$x^{2}-20x+100=-570+100$$

-570 ni 100 ga qo'shish.

$$x^{2}-20x+100=-470$$

x^{2}-20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-10\right)^{2}=-470$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{-470}$$

Qisqartirish.

$$x-10=\sqrt{470}i x-10=-\sqrt{470}i$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x=10+\sqrt{470}i x=-\sqrt{470}i+10$$