x uchun yechish
x=-70
x=5
Grafik
Baham ko'rish
Klipbordga nusxa olish
6000-325x-5x^{2}=4250
15-x ga 400+5x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
6000-325x-5x^{2}-4250=0
Ikkala tarafdan 4250 ni ayirish.
1750-325x-5x^{2}=0
1750 olish uchun 6000 dan 4250 ni ayirish.
-5x^{2}-325x+1750=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=\frac{-\left(-325\right)±\sqrt{\left(-325\right)^{2}-4\left(-5\right)\times 1750}}{2\left(-5\right)}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -5 ni a, -325 ni b va 1750 ni c bilan almashtiring.
x=\frac{-\left(-325\right)±\sqrt{105625-4\left(-5\right)\times 1750}}{2\left(-5\right)}
-325 kvadratini chiqarish.
x=\frac{-\left(-325\right)±\sqrt{105625+20\times 1750}}{2\left(-5\right)}
-4 ni -5 marotabaga ko'paytirish.
x=\frac{-\left(-325\right)±\sqrt{105625+35000}}{2\left(-5\right)}
20 ni 1750 marotabaga ko'paytirish.
x=\frac{-\left(-325\right)±\sqrt{140625}}{2\left(-5\right)}
105625 ni 35000 ga qo'shish.
x=\frac{-\left(-325\right)±375}{2\left(-5\right)}
140625 ning kvadrat ildizini chiqarish.
x=\frac{325±375}{2\left(-5\right)}
-325 ning teskarisi 325 ga teng.
x=\frac{325±375}{-10}
2 ni -5 marotabaga ko'paytirish.
x=\frac{700}{-10}
x=\frac{325±375}{-10} tenglamasini yeching, bunda ± musbat. 325 ni 375 ga qo'shish.
x=-70
700 ni -10 ga bo'lish.
x=-\frac{50}{-10}
x=\frac{325±375}{-10} tenglamasini yeching, bunda ± manfiy. 325 dan 375 ni ayirish.
x=5
-50 ni -10 ga bo'lish.
x=-70 x=5
Tenglama yechildi.
6000-325x-5x^{2}=4250
15-x ga 400+5x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
-325x-5x^{2}=4250-6000
Ikkala tarafdan 6000 ni ayirish.
-325x-5x^{2}=-1750
-1750 olish uchun 4250 dan 6000 ni ayirish.
-5x^{2}-325x=-1750
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
\frac{-5x^{2}-325x}{-5}=-\frac{1750}{-5}
Ikki tarafini -5 ga bo‘ling.
x^{2}+\left(-\frac{325}{-5}\right)x=-\frac{1750}{-5}
-5 ga bo'lish -5 ga ko'paytirishni bekor qiladi.
x^{2}+65x=-\frac{1750}{-5}
-325 ni -5 ga bo'lish.
x^{2}+65x=350
-1750 ni -5 ga bo'lish.
x^{2}+65x+\left(\frac{65}{2}\right)^{2}=350+\left(\frac{65}{2}\right)^{2}
65 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{65}{2} olish uchun. Keyin, \frac{65}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+65x+\frac{4225}{4}=350+\frac{4225}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{65}{2} kvadratini chiqarish.
x^{2}+65x+\frac{4225}{4}=\frac{5625}{4}
350 ni \frac{4225}{4} ga qo'shish.
\left(x+\frac{65}{2}\right)^{2}=\frac{5625}{4}
x^{2}+65x+\frac{4225}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x+\frac{65}{2}\right)^{2}}=\sqrt{\frac{5625}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{65}{2}=\frac{75}{2} x+\frac{65}{2}=-\frac{75}{2}
Qisqartirish.
x=5 x=-70
Tenglamaning ikkala tarafidan \frac{65}{2} ni ayirish.
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