x uchun yechish
x=\frac{\sqrt{19}-3}{2}\approx 0,679449472
x=\frac{-\sqrt{19}-3}{2}\approx -3,679449472
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Klipbordga nusxa olish
2x^{2}+6x-5=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{-6±\sqrt{6^{2}-4\times 2\left(-5\right)}}{2\times 2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 6 ni b va -5 ni c bilan almashtiring.
x=\frac{-6±\sqrt{36-4\times 2\left(-5\right)}}{2\times 2}
6 kvadratini chiqarish.
x=\frac{-6±\sqrt{36-8\left(-5\right)}}{2\times 2}
-4 ni 2 marotabaga ko'paytirish.
x=\frac{-6±\sqrt{36+40}}{2\times 2}
-8 ni -5 marotabaga ko'paytirish.
x=\frac{-6±\sqrt{76}}{2\times 2}
36 ni 40 ga qo'shish.
x=\frac{-6±2\sqrt{19}}{2\times 2}
76 ning kvadrat ildizini chiqarish.
x=\frac{-6±2\sqrt{19}}{4}
2 ni 2 marotabaga ko'paytirish.
x=\frac{2\sqrt{19}-6}{4}
x=\frac{-6±2\sqrt{19}}{4} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{19} ga qo'shish.
x=\frac{\sqrt{19}-3}{2}
-6+2\sqrt{19} ni 4 ga bo'lish.
x=\frac{-2\sqrt{19}-6}{4}
x=\frac{-6±2\sqrt{19}}{4} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{19} ni ayirish.
x=\frac{-\sqrt{19}-3}{2}
-6-2\sqrt{19} ni 4 ga bo'lish.
x=\frac{\sqrt{19}-3}{2} x=\frac{-\sqrt{19}-3}{2}
Tenglama yechildi.
2x^{2}+6x-5=0
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
2x^{2}+6x-5-\left(-5\right)=-\left(-5\right)
5 ni tenglamaning ikkala tarafiga qo'shish.
2x^{2}+6x=-\left(-5\right)
O‘zidan -5 ayirilsa 0 qoladi.
2x^{2}+6x=5
0 dan -5 ni ayirish.
\frac{2x^{2}+6x}{2}=\frac{5}{2}
Ikki tarafini 2 ga bo‘ling.
x^{2}+\frac{6}{2}x=\frac{5}{2}
2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.
x^{2}+3x=\frac{5}{2}
6 ni 2 ga bo'lish.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\frac{5}{2}+\left(\frac{3}{2}\right)^{2}
3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+3x+\frac{9}{4}=\frac{5}{2}+\frac{9}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.
x^{2}+3x+\frac{9}{4}=\frac{19}{4}
Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{2} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.
\left(x+\frac{3}{2}\right)^{2}=\frac{19}{4}
x^{2}+3x+\frac{9}{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{3}{2}\right)^{2}}=\sqrt{\frac{19}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{3}{2}=\frac{\sqrt{19}}{2} x+\frac{3}{2}=-\frac{\sqrt{19}}{2}
Qisqartirish.
x=\frac{\sqrt{19}-3}{2} x=\frac{-\sqrt{19}-3}{2}
Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.
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