20x=8*x^2/2 eching

$$20x= \frac{ 8 \times { x }^{ 2 } }{ 2 }$$

x uchun yechish

$$x=5$$

$$x=0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$40x=8x^{2}$$

Ikkala tarafdan 8x^{2} ni ayirish.

$$40x-8x^{2}=0$$

x omili.

$$x\left(40-8x\right)=0$$

Tenglamani yechish uchun x=0 va 40-8x=0 ni yeching.

$$x=0 x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$40x=8x^{2}$$

Ikkala tarafdan 8x^{2} ni ayirish.

$$40x-8x^{2}=0$$

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.

$$-8x^{2}+40x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -8 ni a, 40 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-40±\sqrt{40^{2}}}{2\left(-8\right)}$$

40^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-40±40}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$x=\frac{-40±40}{-16}$$

x=\frac{-40±40}{-16} tenglamasini yeching, bunda ± musbat. -40 ni 40 ga qo'shish.

$$x=\frac{0}{-16}$$

0 ni -16 ga bo'lish.

$$x=0$$

x=\frac{-40±40}{-16} tenglamasini yeching, bunda ± manfiy. -40 dan 40 ni ayirish.

$$x=-\frac{80}{-16}$$

-80 ni -16 ga bo'lish.

$$x=5$$

Tenglama yechildi.

$$x=0 x=5$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$40x=8x^{2}$$

Ikkala tarafdan 8x^{2} ni ayirish.

$$40x-8x^{2}=0$$

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

$$-8x^{2}+40x=0$$

Ikki tarafini -8 ga bo‘ling.

$$\frac{-8x^{2}+40x}{-8}=\frac{0}{-8}$$

-8 ga bo'lish -8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{40}{-8}x=\frac{0}{-8}$$

40 ni -8 ga bo'lish.

$$x^{2}-5x=\frac{0}{-8}$$

0 ni -8 ga bo'lish.

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

-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.

$$x=5 x=0$$