44+x^2-x=2 eching

$$44+ { x }^{ 2 } -x=2$$

x uchun yechish (complex solution)

$$x=\frac{1+\sqrt{167}i}{2}\approx 0,5+6,461423992i$$

$$x=\frac{-\sqrt{167}i+1}{2}\approx 0,5-6,461423992i$$

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.

$$x^{2}-x+44=2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x^{2}-x+44-2=2-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x^{2}-x+44-2=0$$

44 dan 2 ni ayirish.

$$x^{2}-x+42=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -1 ni b va 42 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 42}}{2}$$

-4 ni 42 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-168}}{2}$$

1 ni -168 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{-167}}{2}$$

-167 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±\sqrt{167}i}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{167}i}{2}$$

x=\frac{1±\sqrt{167}i}{2} tenglamasini yeching, bunda ± musbat. 1 ni i\sqrt{167} ga qo'shish.

$$x=\frac{1+\sqrt{167}i}{2}$$

x=\frac{1±\sqrt{167}i}{2} tenglamasini yeching, bunda ± manfiy. 1 dan i\sqrt{167} ni ayirish.

$$x=\frac{-\sqrt{167}i+1}{2}$$

Tenglama yechildi.

$$x=\frac{1+\sqrt{167}i}{2} x=\frac{-\sqrt{167}i+1}{2}$$

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.

$$x^{2}-x+44=2$$

Tenglamaning ikkala tarafidan 44 ni ayirish.

$$x^{2}-x+44-44=2-44$$

O‘zidan 44 ayirilsa 0 qoladi.

$$x^{2}-x=2-44$$

2 dan 44 ni ayirish.

$$x^{2}-x=-42$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-42+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=-42+\frac{1}{4}$$

-42 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=-\frac{167}{4}$$

x^{2}-x+\frac{1}{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.

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{167}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{167}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{167}i}{2} x-\frac{1}{2}=-\frac{\sqrt{167}i}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1+\sqrt{167}i}{2} x=\frac{-\sqrt{167}i+1}{2}$$