0=x^2-x+156 eching

$$0 = x ^ { 2 } - x + 156$$

x uchun yechish (complex solution)

$$x=\frac{1+\sqrt{623}i}{2}\approx 0,5+12,479983974i$$

$$x=\frac{-\sqrt{623}i+1}{2}\approx 0,5-12,479983974i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-x+156=0$$

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 156 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 156}}{2}$$

-4 ni 156 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-624}}{2}$$

1 ni -624 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{-623}}{2}$$

-623 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±\sqrt{623}i}{2}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{623}i}{2}$$

x=\frac{1±\sqrt{623}i}{2} tenglamasini yeching, bunda ± musbat. 1 ni i\sqrt{623} ga qo'shish.

$$x=\frac{1+\sqrt{623}i}{2}$$

x=\frac{1±\sqrt{623}i}{2} tenglamasini yeching, bunda ± manfiy. 1 dan i\sqrt{623} ni ayirish.

$$x=\frac{-\sqrt{623}i+1}{2}$$

Tenglama yechildi.

$$x=\frac{1+\sqrt{623}i}{2} x=\frac{-\sqrt{623}i+1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-x+156=0$$

Ikkala tarafdan 156 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-x=-156$$

-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.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-156+\left(-\frac{1}{2}\right)^{2}$$

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

$$x^{2}-x+\frac{1}{4}=-156+\frac{1}{4}$$

-156 ni \frac{1}{4} ga qo'shish.

$$x^{2}-x+\frac{1}{4}=-\frac{623}{4}$$

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.

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{623}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{623}{4}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{\sqrt{623}i}{2} x-\frac{1}{2}=-\frac{\sqrt{623}i}{2}$$

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

$$x=\frac{1+\sqrt{623}i}{2} x=\frac{-\sqrt{623}i+1}{2}$$