(600+10x)(10+x)=10000 eching

$$(600+10x)(10+x)=10000$$

x uchun yechish

$$x=5\sqrt{65}-35\approx 5,311288741$$

$$x=-5\sqrt{65}-35\approx -75,311288741$$

Kvadrat tenglamalaridan foydalanish qoidalari

600+10x ga 10+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6000+700x+10x^{2}=10000$$

Ikkala tarafdan 10000 ni ayirish.

$$6000+700x+10x^{2}-10000=0$$

-4000 olish uchun 6000 dan 10000 ni ayirish.

$$-4000+700x+10x^{2}=0$$

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.

$$10x^{2}+700x-4000=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, 700 ni b va -4000 ni c bilan almashtiring.

$$x=\frac{-700±\sqrt{700^{2}-4\times 10\left(-4000\right)}}{2\times 10}$$

700 kvadratini chiqarish.

$$x=\frac{-700±\sqrt{490000-4\times 10\left(-4000\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$x=\frac{-700±\sqrt{490000-40\left(-4000\right)}}{2\times 10}$$

-40 ni -4000 marotabaga ko'paytirish.

$$x=\frac{-700±\sqrt{490000+160000}}{2\times 10}$$

490000 ni 160000 ga qo'shish.

$$x=\frac{-700±\sqrt{650000}}{2\times 10}$$

650000 ning kvadrat ildizini chiqarish.

$$x=\frac{-700±100\sqrt{65}}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{-700±100\sqrt{65}}{20}$$

x=\frac{-700±100\sqrt{65}}{20} tenglamasini yeching, bunda ± musbat. -700 ni 100\sqrt{65} ga qo'shish.

$$x=\frac{100\sqrt{65}-700}{20}$$

-700+100\sqrt{65} ni 20 ga bo'lish.

$$x=5\sqrt{65}-35$$

x=\frac{-700±100\sqrt{65}}{20} tenglamasini yeching, bunda ± manfiy. -700 dan 100\sqrt{65} ni ayirish.

$$x=\frac{-100\sqrt{65}-700}{20}$$

-700-100\sqrt{65} ni 20 ga bo'lish.

$$x=-5\sqrt{65}-35$$

Tenglama yechildi.

$$x=5\sqrt{65}-35 x=-5\sqrt{65}-35$$

Kvadratni yakunlash bo'yicha qadamlar

600+10x ga 10+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$6000+700x+10x^{2}=10000$$

Ikkala tarafdan 6000 ni ayirish.

$$700x+10x^{2}=10000-6000$$

4000 olish uchun 10000 dan 6000 ni ayirish.

$$700x+10x^{2}=4000$$

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

$$10x^{2}+700x=4000$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10x^{2}+700x}{10}=\frac{4000}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{700}{10}x=\frac{4000}{10}$$

700 ni 10 ga bo'lish.

$$x^{2}+70x=\frac{4000}{10}$$

4000 ni 10 ga bo'lish.

$$x^{2}+70x=400$$

70 ni bo‘lish, x shartining koeffitsienti, 2 ga 35 olish uchun. Keyin, 35 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+70x+35^{2}=400+35^{2}$$

35 kvadratini chiqarish.

$$x^{2}+70x+1225=400+1225$$

400 ni 1225 ga qo'shish.

$$x^{2}+70x+1225=1625$$

x^{2}+70x+1225 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+35\right)^{2}=1625$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+35\right)^{2}}=\sqrt{1625}$$

Qisqartirish.

$$x+35=5\sqrt{65} x+35=-5\sqrt{65}$$

Tenglamaning ikkala tarafidan 35 ni ayirish.

$$x=5\sqrt{65}-35 x=-5\sqrt{65}-35$$