(12-2x+1)x=80 eching

$$(12-2x+1)x=80$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{471}i+13}{4}\approx 3,25-5,425633604i$$

$$x=\frac{13+\sqrt{471}i}{4}\approx 3,25+5,425633604i$$

Kvadrat tenglamalaridan foydalanish qoidalari

13 olish uchun 12 va 1'ni qo'shing.

$$\left(13-2x\right)x=80$$

13-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$13x-2x^{2}=80$$

Ikkala tarafdan 80 ni ayirish.

$$13x-2x^{2}-80=0$$

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.

$$-2x^{2}+13x-80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 13 ni b va -80 ni c bilan almashtiring.

$$x=\frac{-13±\sqrt{13^{2}-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

13 kvadratini chiqarish.

$$x=\frac{-13±\sqrt{169-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169+8\left(-80\right)}}{2\left(-2\right)}$$

8 ni -80 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169-640}}{2\left(-2\right)}$$

169 ni -640 ga qo'shish.

$$x=\frac{-13±\sqrt{-471}}{2\left(-2\right)}$$

-471 ning kvadrat ildizini chiqarish.

$$x=\frac{-13±\sqrt{471}i}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{471}i}{-4}$$

x=\frac{-13±\sqrt{471}i}{-4} tenglamasini yeching, bunda ± musbat. -13 ni i\sqrt{471} ga qo'shish.

$$x=\frac{-13+\sqrt{471}i}{-4}$$

-13+i\sqrt{471} ni -4 ga bo'lish.

$$x=\frac{-\sqrt{471}i+13}{4}$$

x=\frac{-13±\sqrt{471}i}{-4} tenglamasini yeching, bunda ± manfiy. -13 dan i\sqrt{471} ni ayirish.

$$x=\frac{-\sqrt{471}i-13}{-4}$$

-13-i\sqrt{471} ni -4 ga bo'lish.

$$x=\frac{13+\sqrt{471}i}{4}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{471}i+13}{4} x=\frac{13+\sqrt{471}i}{4}$$

Kvadratni yakunlash bo'yicha qadamlar

13 olish uchun 12 va 1'ni qo'shing.

$$\left(13-2x\right)x=80$$

13-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$13x-2x^{2}=80$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-2x^{2}+13x=80$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+13x}{-2}=\frac{80}{-2}$$

-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{13}{-2}x=\frac{80}{-2}$$

13 ni -2 ga bo'lish.

$$x^{2}-\frac{13}{2}x=\frac{80}{-2}$$

80 ni -2 ga bo'lish.

$$x^{2}-\frac{13}{2}x=-40$$

-\frac{13}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{4} olish uchun. Keyin, -\frac{13}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{13}{2}x+\left(-\frac{13}{4}\right)^{2}=-40+\left(-\frac{13}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{4} kvadratini chiqarish.

$$x^{2}-\frac{13}{2}x+\frac{169}{16}=-40+\frac{169}{16}$$

-40 ni \frac{169}{16} ga qo'shish.

$$x^{2}-\frac{13}{2}x+\frac{169}{16}=-\frac{471}{16}$$

x^{2}-\frac{13}{2}x+\frac{169}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{13}{4}\right)^{2}=-\frac{471}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{13}{4}\right)^{2}}=\sqrt{-\frac{471}{16}}$$

Qisqartirish.

$$x-\frac{13}{4}=\frac{\sqrt{471}i}{4} x-\frac{13}{4}=-\frac{\sqrt{471}i}{4}$$

\frac{13}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{13+\sqrt{471}i}{4} x=\frac{-\sqrt{471}i+13}{4}$$