(x)=x^2-2x/2+3 eching

$$( x ) = \frac { x ^ { 2 } - 2 x } { 2 + 3 }$$

x uchun yechish

$$x=7$$

$$x=0$$

Faktorlash qadamlari

5 olish uchun 2 va 3'ni qo'shing.

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

\frac{1}{5}x^{2}-\frac{2}{5}x natijani olish uchun x^{2}-2x ning har bir ifodasini 5 ga bo‘ling.

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

Ikkala tarafdan \frac{1}{5}x^{2} ni ayirish.

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

\frac{2}{5}x ni ikki tarafga qo’shing.

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

\frac{7}{5}x ni olish uchun x va \frac{2}{5}x ni birlashtirish.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

x omili.

$$x\left(\frac{7}{5}-\frac{1}{5}x\right)=0$$

Tenglamani yechish uchun x=0 va \frac{7-x}{5}=0 ni yeching.

$$x=0 x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

5 olish uchun 2 va 3'ni qo'shing.

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

\frac{1}{5}x^{2}-\frac{2}{5}x natijani olish uchun x^{2}-2x ning har bir ifodasini 5 ga bo‘ling.

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

Ikkala tarafdan \frac{1}{5}x^{2} ni ayirish.

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

\frac{2}{5}x ni ikki tarafga qo’shing.

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

\frac{7}{5}x ni olish uchun x va \frac{2}{5}x ni birlashtirish.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

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.

$$-\frac{1}{5}x^{2}+\frac{7}{5}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{1}{5} ni a, \frac{7}{5} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\frac{7}{5}±\sqrt{\left(\frac{7}{5}\right)^{2}}}{2\left(-\frac{1}{5}\right)}$$

\left(\frac{7}{5}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{7}{5}±\frac{7}{5}}{2\left(-\frac{1}{5}\right)}$$

2 ni -\frac{1}{5} marotabaga ko'paytirish.

$$x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}}$$

x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{7}{5} ni \frac{7}{5} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{0}{-\frac{2}{5}}$$

0 ni -\frac{2}{5} ga bo'lish 0 ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=0$$

x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{7}{5} ni -\frac{7}{5} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{\frac{14}{5}}{-\frac{2}{5}}$$

-\frac{14}{5} ni -\frac{2}{5} ga bo'lish -\frac{14}{5} ga k'paytirish -\frac{2}{5} ga qaytarish.

$$x=7$$

Tenglama yechildi.

$$x=0 x=7$$

Kvadratni yakunlash bo'yicha qadamlar

5 olish uchun 2 va 3'ni qo'shing.

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

\frac{1}{5}x^{2}-\frac{2}{5}x natijani olish uchun x^{2}-2x ning har bir ifodasini 5 ga bo‘ling.

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

Ikkala tarafdan \frac{1}{5}x^{2} ni ayirish.

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

\frac{2}{5}x ni ikki tarafga qo’shing.

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

\frac{7}{5}x ni olish uchun x va \frac{2}{5}x ni birlashtirish.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

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

$$-\frac{1}{5}x^{2}+\frac{7}{5}x=0$$

Ikkala tarafini -5 ga ko‘paytiring.

$$\frac{-\frac{1}{5}x^{2}+\frac{7}{5}x}{-\frac{1}{5}}=\frac{0}{-\frac{1}{5}}$$

-\frac{1}{5} ga bo'lish -\frac{1}{5} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{\frac{7}{5}}{-\frac{1}{5}}x=\frac{0}{-\frac{1}{5}}$$

\frac{7}{5} ni -\frac{1}{5} ga bo'lish \frac{7}{5} ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}-7x=\frac{0}{-\frac{1}{5}}$$

0 ni -\frac{1}{5} ga bo'lish 0 ga k'paytirish -\frac{1}{5} ga qaytarish.

$$x^{2}-7x=0$$

-7 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{2} olish uchun. Keyin, -\frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

x^{2}-7x+\frac{49}{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.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=0$$