20left(left(x-2right)left(60-x-2right)-16right)=14240 eching

$$20 \left( \left( x-2 \right) \left( 60-x-2 \right) -16 \right) = 14240$$

x uchun yechish

$$x=2\sqrt{14}+30\approx 37,483314774$$

$$x=30-2\sqrt{14}\approx 22,516685226$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 20 ga bo‘ling.

$$\left(x-2\right)\left(60-x-2\right)-16=\frac{14240}{20}$$

712 ni olish uchun 14240 ni 20 ga bo‘ling.

$$\left(x-2\right)\left(60-x-2\right)-16=712$$

58 olish uchun 60 dan 2 ni ayirish.

$$\left(x-2\right)\left(58-x\right)-16=712$$

x-2 ga 58-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$60x-x^{2}-116-16=712$$

-132 olish uchun -116 dan 16 ni ayirish.

$$60x-x^{2}-132=712$$

Ikkala tarafdan 712 ni ayirish.

$$60x-x^{2}-132-712=0$$

-844 olish uchun -132 dan 712 ni ayirish.

$$60x-x^{2}-844=0$$

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.

$$-x^{2}+60x-844=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 60 ni b va -844 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}-4\left(-1\right)\left(-844\right)}}{2\left(-1\right)}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\left(-1\right)\left(-844\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+4\left(-844\right)}}{2\left(-1\right)}$$

4 ni -844 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600-3376}}{2\left(-1\right)}$$

3600 ni -3376 ga qo'shish.

$$x=\frac{-60±\sqrt{224}}{2\left(-1\right)}$$

224 ning kvadrat ildizini chiqarish.

$$x=\frac{-60±4\sqrt{14}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-60±4\sqrt{14}}{-2}$$

x=\frac{-60±4\sqrt{14}}{-2} tenglamasini yeching, bunda ± musbat. -60 ni 4\sqrt{14} ga qo'shish.

$$x=\frac{4\sqrt{14}-60}{-2}$$

-60+4\sqrt{14} ni -2 ga bo'lish.

$$x=30-2\sqrt{14}$$

x=\frac{-60±4\sqrt{14}}{-2} tenglamasini yeching, bunda ± manfiy. -60 dan 4\sqrt{14} ni ayirish.

$$x=\frac{-4\sqrt{14}-60}{-2}$$

-60-4\sqrt{14} ni -2 ga bo'lish.

$$x=2\sqrt{14}+30$$

Tenglama yechildi.

$$x=30-2\sqrt{14} x=2\sqrt{14}+30$$

Kvadratni yakunlash bo'yicha qadamlar

Ikki tarafini 20 ga bo‘ling.

$$\left(x-2\right)\left(60-x-2\right)-16=\frac{14240}{20}$$

712 ni olish uchun 14240 ni 20 ga bo‘ling.

$$\left(x-2\right)\left(60-x-2\right)-16=712$$

58 olish uchun 60 dan 2 ni ayirish.

$$\left(x-2\right)\left(58-x\right)-16=712$$

x-2 ga 58-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$60x-x^{2}-116-16=712$$

-132 olish uchun -116 dan 16 ni ayirish.

$$60x-x^{2}-132=712$$

132 ni ikki tarafga qo’shing.

$$60x-x^{2}=712+132$$

844 olish uchun 712 va 132'ni qo'shing.

$$60x-x^{2}=844$$

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

$$-x^{2}+60x=844$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+60x}{-1}=\frac{844}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{60}{-1}x=\frac{844}{-1}$$

60 ni -1 ga bo'lish.

$$x^{2}-60x=\frac{844}{-1}$$

844 ni -1 ga bo'lish.

$$x^{2}-60x=-844$$

-60 ni bo‘lish, x shartining koeffitsienti, 2 ga -30 olish uchun. Keyin, -30 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-60x+\left(-30\right)^{2}=-844+\left(-30\right)^{2}$$

-30 kvadratini chiqarish.

$$x^{2}-60x+900=-844+900$$

-844 ni 900 ga qo'shish.

$$x^{2}-60x+900=56$$

x^{2}-60x+900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-30\right)^{2}=56$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{56}$$

Qisqartirish.

$$x-30=2\sqrt{14} x-30=-2\sqrt{14}$$

30 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{14}+30 x=30-2\sqrt{14}$$