(20-2x)*(12-2x)=180 eching

$$(20-2x) \times (12-2x)=180$$

x uchun yechish

$$x=15$$

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

20-2x ga 12-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$240-64x+4x^{2}=180$$

Ikkala tarafdan 180 ni ayirish.

$$240-64x+4x^{2}-180=0$$

60 olish uchun 240 dan 180 ni ayirish.

$$60-64x+4x^{2}=0$$

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.

$$4x^{2}-64x+60=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -64 ni b va 60 ni c bilan almashtiring.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 4\times 60}}{2\times 4}$$

-64 kvadratini chiqarish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-4\times 4\times 60}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-16\times 60}}{2\times 4}$$

-16 ni 60 marotabaga ko'paytirish.

$$x=\frac{-\left(-64\right)±\sqrt{4096-960}}{2\times 4}$$

4096 ni -960 ga qo'shish.

$$x=\frac{-\left(-64\right)±\sqrt{3136}}{2\times 4}$$

3136 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-64\right)±56}{2\times 4}$$

-64 ning teskarisi 64 ga teng.

$$x=\frac{64±56}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{64±56}{8}$$

x=\frac{64±56}{8} tenglamasini yeching, bunda ± musbat. 64 ni 56 ga qo'shish.

$$x=\frac{120}{8}$$

120 ni 8 ga bo'lish.

$$x=15$$

x=\frac{64±56}{8} tenglamasini yeching, bunda ± manfiy. 64 dan 56 ni ayirish.

$$x=\frac{8}{8}$$

8 ni 8 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=15 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

20-2x ga 12-2x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$240-64x+4x^{2}=180$$

Ikkala tarafdan 240 ni ayirish.

$$-64x+4x^{2}=180-240$$

-60 olish uchun 180 dan 240 ni ayirish.

$$-64x+4x^{2}=-60$$

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

$$4x^{2}-64x=-60$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-64x}{4}=-\frac{60}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{64}{4}\right)x=-\frac{60}{4}$$

-64 ni 4 ga bo'lish.

$$x^{2}-16x=-\frac{60}{4}$$

-60 ni 4 ga bo'lish.

$$x^{2}-16x=-15$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-16x+\left(-8\right)^{2}=-15+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=-15+64$$

-15 ni 64 ga qo'shish.

$$x^{2}-16x+64=49$$

x^{2}-16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-8\right)^{2}=49$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{49}$$

Qisqartirish.

$$x-8=7 x-8=-7$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=15 x=1$$