x-x^2=5/18 eching

$$x - x ^ { 2 } = \frac { 5 } { 18 }$$

x uchun yechish (complex solution)

$$x=\frac{1}{2}+\frac{1}{6}i\approx 0,5+0,166666667i$$

$$x=\frac{1}{2}-\frac{1}{6}i\approx 0,5-0,166666667i$$

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.

$$-x^{2}+x=\frac{5}{18}$$

Tenglamaning ikkala tarafidan \frac{5}{18} ni ayirish.

$$-x^{2}+x-\frac{5}{18}=\frac{5}{18}-\frac{5}{18}$$

O‘zidan \frac{5}{18} ayirilsa 0 qoladi.

$$-x^{2}+x-\frac{5}{18}=0$$

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 -\frac{5}{18} ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\left(-\frac{5}{18}\right)}}{2\left(-1\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-1\right)\left(-\frac{5}{18}\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+4\left(-\frac{5}{18}\right)}}{2\left(-1\right)}$$

4 ni -\frac{5}{18} marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1-\frac{10}{9}}}{2\left(-1\right)}$$

1 ni -\frac{10}{9} ga qo'shish.

$$x=\frac{-1±\sqrt{-\frac{1}{9}}}{2\left(-1\right)}$$

-\frac{1}{9} ning kvadrat ildizini chiqarish.

$$x=\frac{-1±\frac{1}{3}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1±\frac{1}{3}i}{-2}$$

x=\frac{-1±\frac{1}{3}i}{-2} tenglamasini yeching, bunda ± musbat. -1 ni \frac{1}{3}i ga qo'shish.

$$x=\frac{-1+\frac{1}{3}i}{-2}$$

-1+\frac{1}{3}i ni -2 ga bo'lish.

$$x=\frac{1}{2}-\frac{1}{6}i$$

x=\frac{-1±\frac{1}{3}i}{-2} tenglamasini yeching, bunda ± manfiy. -1 dan \frac{1}{3}i ni ayirish.

$$x=\frac{-1-\frac{1}{3}i}{-2}$$

-1-\frac{1}{3}i ni -2 ga bo'lish.

$$x=\frac{1}{2}+\frac{1}{6}i$$

Tenglama yechildi.

$$x=\frac{1}{2}-\frac{1}{6}i x=\frac{1}{2}+\frac{1}{6}i$$

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.

$$-x^{2}+x=\frac{5}{18}$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+x}{-1}=\frac{\frac{5}{18}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1}{-1}x=\frac{\frac{5}{18}}{-1}$$

1 ni -1 ga bo'lish.

$$x^{2}-x=\frac{\frac{5}{18}}{-1}$$

\frac{5}{18} ni -1 ga bo'lish.

$$x^{2}-x=-\frac{5}{18}$$

-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.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=-\frac{5}{18}+\left(-\frac{1}{2}\right)^{2}$$

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

$$x^{2}-x+\frac{1}{4}=-\frac{5}{18}+\frac{1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{5}{18} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-x+\frac{1}{4}=-\frac{1}{36}$$

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.

$$\left(x-\frac{1}{2}\right)^{2}=-\frac{1}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{1}{36}}$$

Qisqartirish.

$$x-\frac{1}{2}=\frac{1}{6}i x-\frac{1}{2}=-\frac{1}{6}i$$

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

$$x=\frac{1}{2}+\frac{1}{6}i x=\frac{1}{2}-\frac{1}{6}i$$