(200-20(x-10)(x-8)=640 eching

$$(200-20(x-10)(x-8)=640$$

x uchun yechish (complex solution)

$$x=9+\sqrt{21}i\approx 9+4,582575695i$$

$$x=-\sqrt{21}i+9\approx 9-4,582575695i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 640 ni ayirish.

$$200-20\left(x-10\right)\left(x-8\right)-640=0$$

-20 ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$200+\left(-20x+200\right)\left(x-8\right)-640=0$$

-20x+200 ga x-8 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$200-20x^{2}+360x-1600-640=0$$

-1400 olish uchun 200 dan 1600 ni ayirish.

$$-1400-20x^{2}+360x-640=0$$

-2040 olish uchun -1400 dan 640 ni ayirish.

$$-2040-20x^{2}+360x=0$$

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.

$$-20x^{2}+360x-2040=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -20 ni a, 360 ni b va -2040 ni c bilan almashtiring.

$$x=\frac{-360±\sqrt{360^{2}-4\left(-20\right)\left(-2040\right)}}{2\left(-20\right)}$$

360 kvadratini chiqarish.

$$x=\frac{-360±\sqrt{129600-4\left(-20\right)\left(-2040\right)}}{2\left(-20\right)}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-360±\sqrt{129600+80\left(-2040\right)}}{2\left(-20\right)}$$

80 ni -2040 marotabaga ko'paytirish.

$$x=\frac{-360±\sqrt{129600-163200}}{2\left(-20\right)}$$

129600 ni -163200 ga qo'shish.

$$x=\frac{-360±\sqrt{-33600}}{2\left(-20\right)}$$

-33600 ning kvadrat ildizini chiqarish.

$$x=\frac{-360±40\sqrt{21}i}{2\left(-20\right)}$$

2 ni -20 marotabaga ko'paytirish.

$$x=\frac{-360±40\sqrt{21}i}{-40}$$

x=\frac{-360±40\sqrt{21}i}{-40} tenglamasini yeching, bunda ± musbat. -360 ni 40i\sqrt{21} ga qo'shish.

$$x=\frac{-360+40\sqrt{21}i}{-40}$$

-360+40i\sqrt{21} ni -40 ga bo'lish.

$$x=-\sqrt{21}i+9$$

x=\frac{-360±40\sqrt{21}i}{-40} tenglamasini yeching, bunda ± manfiy. -360 dan 40i\sqrt{21} ni ayirish.

$$x=\frac{-40\sqrt{21}i-360}{-40}$$

-360-40i\sqrt{21} ni -40 ga bo'lish.

$$x=9+\sqrt{21}i$$

Tenglama yechildi.

$$x=-\sqrt{21}i+9 x=9+\sqrt{21}i$$

Kvadratni yakunlash bo'yicha qadamlar

-20 hosil qilish uchun -1 va 20 ni ko'paytirish.

$$200-20\left(x-10\right)\left(x-8\right)=640$$

-20 ga x-10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$200+\left(-20x+200\right)\left(x-8\right)=640$$

-20x+200 ga x-8 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$200-20x^{2}+360x-1600=640$$

-1400 olish uchun 200 dan 1600 ni ayirish.

$$-1400-20x^{2}+360x=640$$

1400 ni ikki tarafga qo’shing.

$$-20x^{2}+360x=640+1400$$

2040 olish uchun 640 va 1400'ni qo'shing.

$$-20x^{2}+360x=2040$$

Ikki tarafini -20 ga bo‘ling.

$$\frac{-20x^{2}+360x}{-20}=\frac{2040}{-20}$$

-20 ga bo'lish -20 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{360}{-20}x=\frac{2040}{-20}$$

360 ni -20 ga bo'lish.

$$x^{2}-18x=\frac{2040}{-20}$$

2040 ni -20 ga bo'lish.

$$x^{2}-18x=-102$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-18x+\left(-9\right)^{2}=-102+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=-102+81$$

-102 ni 81 ga qo'shish.

$$x^{2}-18x+81=-21$$

x^{2}-18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-9\right)^{2}=-21$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{-21}$$

Qisqartirish.

$$x-9=\sqrt{21}i x-9=-\sqrt{21}i$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=9+\sqrt{21}i x=-\sqrt{21}i+9$$