x^2/4-x+5=0 eching

$$\frac { x ^ { 2 } } { 4 } - x + 5 = 0$$

x uchun yechish (complex solution)

$$x=2+4i$$

$$x=2-4i$$

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.

$$\frac{1}{4}x^{2}-x+5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{4} ni a, -1 ni b va 5 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{1}{4}\times 5}}{2\times \frac{1}{4}}$$

-4 ni \frac{1}{4} marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-5}}{2\times \frac{1}{4}}$$

1 ni -5 ga qo'shish.

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

-4 ning kvadrat ildizini chiqarish.

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

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±2i}{2\times \frac{1}{4}}$$

2 ni \frac{1}{4} marotabaga ko'paytirish.

$$x=\frac{1±2i}{\frac{1}{2}}$$

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

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

1+2i ni \frac{1}{2} ga bo'lish 1+2i ga k'paytirish \frac{1}{2} ga qaytarish.

$$x=2+4i$$

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

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

1-2i ni \frac{1}{2} ga bo'lish 1-2i ga k'paytirish \frac{1}{2} ga qaytarish.

$$x=2-4i$$

Tenglama yechildi.

$$x=2+4i x=2-4i$$

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.

$$\frac{1}{4}x^{2}-x+5=0$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$\frac{1}{4}x^{2}-x+5-5=-5$$

O‘zidan 5 ayirilsa 0 qoladi.

$$\frac{1}{4}x^{2}-x=-5$$

Ikkala tarafini 4 ga ko‘paytiring.

$$\frac{\frac{1}{4}x^{2}-x}{\frac{1}{4}}=-\frac{5}{\frac{1}{4}}$$

\frac{1}{4} ga bo'lish \frac{1}{4} ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{1}{\frac{1}{4}}\right)x=-\frac{5}{\frac{1}{4}}$$

-1 ni \frac{1}{4} ga bo'lish -1 ga k'paytirish \frac{1}{4} ga qaytarish.

$$x^{2}-4x=-\frac{5}{\frac{1}{4}}$$

-5 ni \frac{1}{4} ga bo'lish -5 ga k'paytirish \frac{1}{4} ga qaytarish.

$$x^{2}-4x=-20$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-4x+\left(-2\right)^{2}=-20+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=-20+4$$

-20 ni 4 ga qo'shish.

$$x^{2}-4x+4=-16$$

x^{2}-4x+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.

$$\left(x-2\right)^{2}=-16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{-16}$$

Qisqartirish.

$$x-2=4i x-2=-4i$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2+4i x=2-4i$$