xx-3=7x-20 eching

$$x x - 3 = 7 x - 20$$

x uchun yechish (complex solution)

$$x=\frac{7+\sqrt{19}i}{2}\approx 3,5+2,179449472i$$

$$x=\frac{-\sqrt{19}i+7}{2}\approx 3,5-2,179449472i$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}-3=7x-20$$

Ikkala tarafdan 7x ni ayirish.

$$x^{2}-3-7x=-20$$

20 ni ikki tarafga qo’shing.

$$x^{2}-3-7x+20=0$$

17 olish uchun -3 va 20'ni qo'shing.

$$x^{2}+17-7x=0$$

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.

$$x^{2}-7x+17=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -7 ni b va 17 ni c bilan almashtiring.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 17}}{2}$$

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 17}}{2}$$

-4 ni 17 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49-68}}{2}$$

49 ni -68 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{-19}}{2}$$

-19 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{19}i}{2}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{19}i}{2}$$

x=\frac{7±\sqrt{19}i}{2} tenglamasini yeching, bunda ± musbat. 7 ni i\sqrt{19} ga qo'shish.

$$x=\frac{7+\sqrt{19}i}{2}$$

x=\frac{7±\sqrt{19}i}{2} tenglamasini yeching, bunda ± manfiy. 7 dan i\sqrt{19} ni ayirish.

$$x=\frac{-\sqrt{19}i+7}{2}$$

Tenglama yechildi.

$$x=\frac{7+\sqrt{19}i}{2} x=\frac{-\sqrt{19}i+7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}-3=7x-20$$

Ikkala tarafdan 7x ni ayirish.

$$x^{2}-3-7x=-20$$

3 ni ikki tarafga qo’shing.

$$x^{2}-7x=-20+3$$

-17 olish uchun -20 va 3'ni qo'shing.

$$x^{2}-7x=-17$$

-7 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{2} olish uchun. Keyin, -\frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-17+\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=-17+\frac{49}{4}$$

-17 ni \frac{49}{4} ga qo'shish.

$$x^{2}-7x+\frac{49}{4}=-\frac{19}{4}$$

x^{2}-7x+\frac{49}{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.

$$\left(x-\frac{7}{2}\right)^{2}=-\frac{19}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{-\frac{19}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{\sqrt{19}i}{2} x-\frac{7}{2}=-\frac{\sqrt{19}i}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{7+\sqrt{19}i}{2} x=\frac{-\sqrt{19}i+7}{2}$$