x^2-5x=0:pi eching

$$x ^ { 2 } - 5 x = 0 : \pi$$

x uchun yechish

$$x=5$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan \frac{0}{\pi } ni ayirish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}-5x ni \frac{\pi }{\pi } marotabaga ko'paytirish.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

\frac{\left(x^{2}-5x\right)\pi }{\pi } va \frac{0}{\pi } da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

\left(x^{2}-5x\right)\pi -0 ichidagi ko‘paytirishlarni bajaring.

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

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

$$-5x+x^{2}=0$$

x omili.

$$x\left(-5+x\right)=0$$

Tenglamani yechish uchun x=0 va -5+x=0 ni yeching.

$$x=0 x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{0}{\pi } ni ayirish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}-5x ni \frac{\pi }{\pi } marotabaga ko'paytirish.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

\frac{\left(x^{2}-5x\right)\pi }{\pi } va \frac{0}{\pi } da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

\left(x^{2}-5x\right)\pi -0 ichidagi ko‘paytirishlarni bajaring.

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

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

$$-5x+x^{2}=0$$

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.

$$x^{2}-5x=0$$

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

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

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

$$x=\frac{-\left(-5\right)±5}{2}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±5}{2}$$

x=\frac{5±5}{2} tenglamasini yeching, bunda ± musbat. 5 ni 5 ga qo'shish.

$$x=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$x=5$$

x=\frac{5±5}{2} tenglamasini yeching, bunda ± manfiy. 5 dan 5 ni ayirish.

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=5 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{0}{\pi } ni ayirish.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{2}-5x ni \frac{\pi }{\pi } marotabaga ko'paytirish.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

\frac{\left(x^{2}-5x\right)\pi }{\pi } va \frac{0}{\pi } da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

\left(x^{2}-5x\right)\pi -0 ichidagi ko‘paytirishlarni bajaring.

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

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

$$-5x+x^{2}=0$$

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

$$x^{2}-5x=0$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=\frac{25}{4}$$

x^{2}-5x+\frac{25}{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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

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

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=0$$