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5x^{2}+8x-7=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{-8±\sqrt{8^{2}-4\times 5\left(-7\right)}}{2\times 5}
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{-8±\sqrt{64-4\times 5\left(-7\right)}}{2\times 5}
8 kvadratini chiqarish.
x=\frac{-8±\sqrt{64-20\left(-7\right)}}{2\times 5}
-4 ni 5 marotabaga ko'paytirish.
x=\frac{-8±\sqrt{64+140}}{2\times 5}
-20 ni -7 marotabaga ko'paytirish.
x=\frac{-8±\sqrt{204}}{2\times 5}
64 ni 140 ga qo'shish.
x=\frac{-8±2\sqrt{51}}{2\times 5}
204 ning kvadrat ildizini chiqarish.
x=\frac{-8±2\sqrt{51}}{10}
2 ni 5 marotabaga ko'paytirish.
x=\frac{2\sqrt{51}-8}{10}
x=\frac{-8±2\sqrt{51}}{10} tenglamasini yeching, bunda ± musbat. -8 ni 2\sqrt{51} ga qo'shish.
x=\frac{\sqrt{51}-4}{5}
-8+2\sqrt{51} ni 10 ga bo'lish.
x=\frac{-2\sqrt{51}-8}{10}
x=\frac{-8±2\sqrt{51}}{10} tenglamasini yeching, bunda ± manfiy. -8 dan 2\sqrt{51} ni ayirish.
x=\frac{-\sqrt{51}-4}{5}
-8-2\sqrt{51} ni 10 ga bo'lish.
5x^{2}+8x-7=5\left(x-\frac{\sqrt{51}-4}{5}\right)\left(x-\frac{-\sqrt{51}-4}{5}\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-4+\sqrt{51}}{5} ga va x_{2} uchun \frac{-4-\sqrt{51}}{5} ga bo‘ling.