27x^2+11x-2 eching

$$27 x ^ { 2 } + 11 x - 2$$

Omil

$$27\left(x-\frac{-\sqrt{337}-11}{54}\right)\left(x-\frac{\sqrt{337}-11}{54}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$27x^{2}+11x-2=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 27\left(-2\right)}}{2\times 27}$$

11 kvadratini chiqarish.

$$x=\frac{-11±\sqrt{121-4\times 27\left(-2\right)}}{2\times 27}$$

-4 ni 27 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121-108\left(-2\right)}}{2\times 27}$$

-108 ni -2 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{121+216}}{2\times 27}$$

121 ni 216 ga qo'shish.

$$x=\frac{-11±\sqrt{337}}{2\times 27}$$

2 ni 27 marotabaga ko'paytirish.

$$x=\frac{-11±\sqrt{337}}{54}$$

x=\frac{-11±\sqrt{337}}{54} tenglamasini yeching, bunda ± musbat. -11 ni \sqrt{337} ga qo'shish.

$$x=\frac{\sqrt{337}-11}{54}$$

x=\frac{-11±\sqrt{337}}{54} tenglamasini yeching, bunda ± manfiy. -11 dan \sqrt{337} ni ayirish.

$$x=\frac{-\sqrt{337}-11}{54}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-11+\sqrt{337}}{54} ga va x_{2} uchun \frac{-11-\sqrt{337}}{54} ga bo‘ling.

$$27x^{2}+11x-2=27\left(x-\frac{\sqrt{337}-11}{54}\right)\left(x-\frac{-\sqrt{337}-11}{54}\right)$$

Baholash

$$27x^{2}+11x-2$$