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x^{2}-3x=-4
Ikkala tarafdan 3x ni ayirish.
x^{2}-3x+4=0
4 ni ikki tarafga qo’shing.
x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 4}}{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 4 ni c bilan almashtiring.
x=\frac{-\left(-3\right)±\sqrt{9-4\times 4}}{2}
-3 kvadratini chiqarish.
x=\frac{-\left(-3\right)±\sqrt{9-16}}{2}
-4 ni 4 marotabaga ko'paytirish.
x=\frac{-\left(-3\right)±\sqrt{-7}}{2}
9 ni -16 ga qo'shish.
x=\frac{-\left(-3\right)±\sqrt{7}i}{2}
-7 ning kvadrat ildizini chiqarish.
x=\frac{3±\sqrt{7}i}{2}
-3 ning teskarisi 3 ga teng.
x=\frac{3+\sqrt{7}i}{2}
x=\frac{3±\sqrt{7}i}{2} tenglamasini yeching, bunda ± musbat. 3 ni i\sqrt{7} ga qo'shish.
x=\frac{-\sqrt{7}i+3}{2}
x=\frac{3±\sqrt{7}i}{2} tenglamasini yeching, bunda ± manfiy. 3 dan i\sqrt{7} ni ayirish.
x=\frac{3+\sqrt{7}i}{2} x=\frac{-\sqrt{7}i+3}{2}
Tenglama yechildi.
x^{2}-3x=-4
Ikkala tarafdan 3x ni ayirish.
x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=-4+\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}=-4+\frac{9}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.
x^{2}-3x+\frac{9}{4}=-\frac{7}{4}
-4 ni \frac{9}{4} ga qo'shish.
\left(x-\frac{3}{2}\right)^{2}=-\frac{7}{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{7}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-\frac{3}{2}=\frac{\sqrt{7}i}{2} x-\frac{3}{2}=-\frac{\sqrt{7}i}{2}
Qisqartirish.
x=\frac{3+\sqrt{7}i}{2} x=\frac{-\sqrt{7}i+3}{2}
\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.