x uchun yechish
x = \frac{\sqrt{7809} - 7}{8} \approx 10,171068305
x=\frac{-\sqrt{7809}-7}{8}\approx -11,921068305
Grafik
Baham ko'rish
Klipbordga nusxa olish
8x^{2}+14x=970
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.
8x^{2}+14x-970=970-970
Tenglamaning ikkala tarafidan 970 ni ayirish.
8x^{2}+14x-970=0
O‘zidan 970 ayirilsa 0 qoladi.
x=\frac{-14±\sqrt{14^{2}-4\times 8\left(-970\right)}}{2\times 8}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 14 ni b va -970 ni c bilan almashtiring.
x=\frac{-14±\sqrt{196-4\times 8\left(-970\right)}}{2\times 8}
14 kvadratini chiqarish.
x=\frac{-14±\sqrt{196-32\left(-970\right)}}{2\times 8}
-4 ni 8 marotabaga ko'paytirish.
x=\frac{-14±\sqrt{196+31040}}{2\times 8}
-32 ni -970 marotabaga ko'paytirish.
x=\frac{-14±\sqrt{31236}}{2\times 8}
196 ni 31040 ga qo'shish.
x=\frac{-14±2\sqrt{7809}}{2\times 8}
31236 ning kvadrat ildizini chiqarish.
x=\frac{-14±2\sqrt{7809}}{16}
2 ni 8 marotabaga ko'paytirish.
x=\frac{2\sqrt{7809}-14}{16}
x=\frac{-14±2\sqrt{7809}}{16} tenglamasini yeching, bunda ± musbat. -14 ni 2\sqrt{7809} ga qo'shish.
x=\frac{\sqrt{7809}-7}{8}
-14+2\sqrt{7809} ni 16 ga bo'lish.
x=\frac{-2\sqrt{7809}-14}{16}
x=\frac{-14±2\sqrt{7809}}{16} tenglamasini yeching, bunda ± manfiy. -14 dan 2\sqrt{7809} ni ayirish.
x=\frac{-\sqrt{7809}-7}{8}
-14-2\sqrt{7809} ni 16 ga bo'lish.
x=\frac{\sqrt{7809}-7}{8} x=\frac{-\sqrt{7809}-7}{8}
Tenglama yechildi.
8x^{2}+14x=970
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
\frac{8x^{2}+14x}{8}=\frac{970}{8}
Ikki tarafini 8 ga bo‘ling.
x^{2}+\frac{14}{8}x=\frac{970}{8}
8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.
x^{2}+\frac{7}{4}x=\frac{970}{8}
\frac{14}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x^{2}+\frac{7}{4}x=\frac{485}{4}
\frac{970}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x^{2}+\frac{7}{4}x+\left(\frac{7}{8}\right)^{2}=\frac{485}{4}+\left(\frac{7}{8}\right)^{2}
\frac{7}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{8} olish uchun. Keyin, \frac{7}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+\frac{7}{4}x+\frac{49}{64}=\frac{485}{4}+\frac{49}{64}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{8} kvadratini chiqarish.
x^{2}+\frac{7}{4}x+\frac{49}{64}=\frac{7809}{64}
Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{485}{4} ni \frac{49}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.
\left(x+\frac{7}{8}\right)^{2}=\frac{7809}{64}
x^{2}+\frac{7}{4}x+\frac{49}{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.
\sqrt{\left(x+\frac{7}{8}\right)^{2}}=\sqrt{\frac{7809}{64}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{7}{8}=\frac{\sqrt{7809}}{8} x+\frac{7}{8}=-\frac{\sqrt{7809}}{8}
Qisqartirish.
x=\frac{\sqrt{7809}-7}{8} x=\frac{-\sqrt{7809}-7}{8}
Tenglamaning ikkala tarafidan \frac{7}{8} ni ayirish.
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