(20-2x)x=42 eching

$$(20-2x)x=42$$

x uchun yechish

$$x=3$$

$$x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

20-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x-2x^{2}=42$$

Ikkala tarafdan 42 ni ayirish.

$$20x-2x^{2}-42=0$$

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.

$$-2x^{2}+20x-42=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 20 ni b va -42 ni c bilan almashtiring.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-2\right)\left(-42\right)}}{2\left(-2\right)}$$

20 kvadratini chiqarish.

$$x=\frac{-20±\sqrt{400-4\left(-2\right)\left(-42\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400+8\left(-42\right)}}{2\left(-2\right)}$$

8 ni -42 marotabaga ko'paytirish.

$$x=\frac{-20±\sqrt{400-336}}{2\left(-2\right)}$$

400 ni -336 ga qo'shish.

$$x=\frac{-20±\sqrt{64}}{2\left(-2\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-20±8}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-20±8}{-4}$$

x=\frac{-20±8}{-4} tenglamasini yeching, bunda ± musbat. -20 ni 8 ga qo'shish.

$$x=-\frac{12}{-4}$$

-12 ni -4 ga bo'lish.

$$x=3$$

x=\frac{-20±8}{-4} tenglamasini yeching, bunda ± manfiy. -20 dan 8 ni ayirish.

$$x=-\frac{28}{-4}$$

-28 ni -4 ga bo'lish.

$$x=7$$

Tenglama yechildi.

$$x=3 x=7$$

Kvadratni yakunlash bo'yicha qadamlar

20-2x ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x-2x^{2}=42$$

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

$$-2x^{2}+20x=42$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+20x}{-2}=\frac{42}{-2}$$

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

$$x^{2}+\frac{20}{-2}x=\frac{42}{-2}$$

20 ni -2 ga bo'lish.

$$x^{2}-10x=\frac{42}{-2}$$

42 ni -2 ga bo'lish.

$$x^{2}-10x=-21$$

-10 ni bo‘lish, x shartining koeffitsienti, 2 ga -5 olish uchun. Keyin, -5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-10x+\left(-5\right)^{2}=-21+\left(-5\right)^{2}$$

-5 kvadratini chiqarish.

$$x^{2}-10x+25=-21+25$$

-21 ni 25 ga qo'shish.

$$x^{2}-10x+25=4$$

x^{2}-10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-5=2 x-5=-2$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=3$$