5x^2-20x+12=x^2+1x-6 eching

$$5 x ^ { 2 } - 20 x + 12 = x ^ { 2 } + 1 x - 6$$

x uchun yechish

$$x = \frac{3 \sqrt{17} + 21}{8} \approx 4,17116461$$

$$x = \frac{21 - 3 \sqrt{17}}{8} \approx 1,07883539$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

$$5x^{2}-20x+12-x^{2}=1x-6$$

4x^{2} ni olish uchun 5x^{2} va -x^{2} ni birlashtirish.

$$4x^{2}-20x+12=1x-6$$

Ikkala tarafdan 1x ni ayirish.

$$4x^{2}-20x+12-x=-6$$

-21x ni olish uchun -20x va -x ni birlashtirish.

$$4x^{2}-21x+12=-6$$

6 ni ikki tarafga qo’shing.

$$4x^{2}-21x+12+6=0$$

18 olish uchun 12 va 6'ni qo'shing.

$$4x^{2}-21x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -21 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 4\times 18}}{2\times 4}$$

-21 kvadratini chiqarish.

$$x=\frac{-\left(-21\right)±\sqrt{441-4\times 4\times 18}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-21\right)±\sqrt{441-16\times 18}}{2\times 4}$$

-16 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-21\right)±\sqrt{441-288}}{2\times 4}$$

441 ni -288 ga qo'shish.

$$x=\frac{-\left(-21\right)±\sqrt{153}}{2\times 4}$$

153 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-21\right)±3\sqrt{17}}{2\times 4}$$

-21 ning teskarisi 21 ga teng.

$$x=\frac{21±3\sqrt{17}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{21±3\sqrt{17}}{8}$$

x=\frac{21±3\sqrt{17}}{8} tenglamasini yeching, bunda ± musbat. 21 ni 3\sqrt{17} ga qo'shish.

$$x=\frac{3\sqrt{17}+21}{8}$$

x=\frac{21±3\sqrt{17}}{8} tenglamasini yeching, bunda ± manfiy. 21 dan 3\sqrt{17} ni ayirish.

$$x=\frac{21-3\sqrt{17}}{8}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{17}+21}{8} x=\frac{21-3\sqrt{17}}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

$$5x^{2}-20x+12-x^{2}=1x-6$$

4x^{2} ni olish uchun 5x^{2} va -x^{2} ni birlashtirish.

$$4x^{2}-20x+12=1x-6$$

Ikkala tarafdan 1x ni ayirish.

$$4x^{2}-20x+12-x=-6$$

-21x ni olish uchun -20x va -x ni birlashtirish.

$$4x^{2}-21x+12=-6$$

Ikkala tarafdan 12 ni ayirish.

$$4x^{2}-21x=-6-12$$

-18 olish uchun -6 dan 12 ni ayirish.

$$4x^{2}-21x=-18$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-21x}{4}=-\frac{18}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{21}{4}x=-\frac{18}{4}$$

\frac{-18}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{21}{4}x=-\frac{9}{2}$$

-\frac{21}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{21}{8} olish uchun. Keyin, -\frac{21}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{21}{4}x+\left(-\frac{21}{8}\right)^{2}=-\frac{9}{2}+\left(-\frac{21}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{21}{8} kvadratini chiqarish.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=-\frac{9}{2}+\frac{441}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{9}{2} ni \frac{441}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=\frac{153}{64}$$

x^{2}-\frac{21}{4}x+\frac{441}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{21}{8}\right)^{2}=\frac{153}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{21}{8}\right)^{2}}=\sqrt{\frac{153}{64}}$$

Qisqartirish.

$$x-\frac{21}{8}=\frac{3\sqrt{17}}{8} x-\frac{21}{8}=-\frac{3\sqrt{17}}{8}$$

\frac{21}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{17}+21}{8} x=\frac{21-3\sqrt{17}}{8}$$