left(40-xright)left(20+2xright)=1200 eching

$$\left( 40-x \right) \left( 20+2x \right) = 1200$$

x uchun yechish

$$x=10$$

$$x=20$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$800+60x-2x^{2}=1200$$

Ikkala tarafdan 1200 ni ayirish.

$$800+60x-2x^{2}-1200=0$$

-400 olish uchun 800 dan 1200 ni ayirish.

$$-400+60x-2x^{2}=0$$

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.

$$-2x^{2}+60x-400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 60 ni b va -400 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}-4\left(-2\right)\left(-400\right)}}{2\left(-2\right)}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\left(-2\right)\left(-400\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+8\left(-400\right)}}{2\left(-2\right)}$$

8 ni -400 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600-3200}}{2\left(-2\right)}$$

3600 ni -3200 ga qo'shish.

$$x=\frac{-60±\sqrt{400}}{2\left(-2\right)}$$

400 ning kvadrat ildizini chiqarish.

$$x=\frac{-60±20}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-60±20}{-4}$$

x=\frac{-60±20}{-4} tenglamasini yeching, bunda ± musbat. -60 ni 20 ga qo'shish.

$$x=-\frac{40}{-4}$$

-40 ni -4 ga bo'lish.

$$x=10$$

x=\frac{-60±20}{-4} tenglamasini yeching, bunda ± manfiy. -60 dan 20 ni ayirish.

$$x=-\frac{80}{-4}$$

-80 ni -4 ga bo'lish.

$$x=20$$

Tenglama yechildi.

$$x=10 x=20$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$800+60x-2x^{2}=1200$$

Ikkala tarafdan 800 ni ayirish.

$$60x-2x^{2}=1200-800$$

400 olish uchun 1200 dan 800 ni ayirish.

$$60x-2x^{2}=400$$

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

$$-2x^{2}+60x=400$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}+60x}{-2}=\frac{400}{-2}$$

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

$$x^{2}+\frac{60}{-2}x=\frac{400}{-2}$$

60 ni -2 ga bo'lish.

$$x^{2}-30x=\frac{400}{-2}$$

400 ni -2 ga bo'lish.

$$x^{2}-30x=-200$$

-30 ni bo‘lish, x shartining koeffitsienti, 2 ga -15 olish uchun. Keyin, -15 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-30x+\left(-15\right)^{2}=-200+\left(-15\right)^{2}$$

-15 kvadratini chiqarish.

$$x^{2}-30x+225=-200+225$$

-200 ni 225 ga qo'shish.

$$x^{2}-30x+225=25$$

x^{2}-30x+225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-15\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-15\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-15=5 x-15=-5$$

15 ni tenglamaning ikkala tarafiga qo'shish.

$$x=20 x=10$$