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x^{2}-x-4=0
Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.
x=\frac{-\left(-1\right)±\sqrt{1-4\left(-4\right)}}{2}
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(-1\right)±\sqrt{1+16}}{2}
-4 ni -4 marotabaga ko'paytirish.
x=\frac{-\left(-1\right)±\sqrt{17}}{2}
1 ni 16 ga qo'shish.
x=\frac{1±\sqrt{17}}{2}
-1 ning teskarisi 1 ga teng.
x=\frac{\sqrt{17}+1}{2}
x=\frac{1±\sqrt{17}}{2} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{17} ga qo'shish.
x=\frac{1-\sqrt{17}}{2}
x=\frac{1±\sqrt{17}}{2} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{17} ni ayirish.
x^{2}-x-4=\left(x-\frac{\sqrt{17}+1}{2}\right)\left(x-\frac{1-\sqrt{17}}{2}\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{17}}{2} ga va x_{2} uchun \frac{1-\sqrt{17}}{2} ga bo‘ling.