x uchun yechish
x=\frac{\sqrt{17}-3}{2}\approx 0,561552813
x=\frac{-\sqrt{17}-3}{2}\approx -3,561552813
Grafik
Viktorina
Quadratic Equation
x(x+2)+x=2
Baham ko'rish
Klipbordga nusxa olish
x^{2}+2x+x=2
x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}+3x=2
3x ni olish uchun 2x va x ni birlashtirish.
x^{2}+3x-2=0
Ikkala tarafdan 2 ni ayirish.
x=\frac{-3±\sqrt{3^{2}-4\left(-2\right)}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 3 ni b va -2 ni c bilan almashtiring.
x=\frac{-3±\sqrt{9-4\left(-2\right)}}{2}
3 kvadratini chiqarish.
x=\frac{-3±\sqrt{9+8}}{2}
-4 ni -2 marotabaga ko'paytirish.
x=\frac{-3±\sqrt{17}}{2}
9 ni 8 ga qo'shish.
x=\frac{\sqrt{17}-3}{2}
x=\frac{-3±\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{17} ga qo'shish.
x=\frac{-\sqrt{17}-3}{2}
x=\frac{-3±\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{17} ni ayirish.
x=\frac{\sqrt{17}-3}{2} x=\frac{-\sqrt{17}-3}{2}
Tenglama yechildi.
x^{2}+2x+x=2
x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
x^{2}+3x=2
3x ni olish uchun 2x va x ni birlashtirish.
x^{2}+3x+\left(\frac{3}{2}\right)^{2}=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}=2+\frac{9}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.
x^{2}+3x+\frac{9}{4}=\frac{17}{4}
2 ni \frac{9}{4} ga qo'shish.
\left(x+\frac{3}{2}\right)^{2}=\frac{17}{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{17}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{3}{2}=\frac{\sqrt{17}}{2} x+\frac{3}{2}=-\frac{\sqrt{17}}{2}
Qisqartirish.
x=\frac{\sqrt{17}-3}{2} x=\frac{-\sqrt{17}-3}{2}
Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.
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