18x^2+31x-40 eching

$$18 x ^ { 2 } + 31 x - 40$$

Omil

$$18\left(x-\frac{-\sqrt{3841}-31}{36}\right)\left(x-\frac{\sqrt{3841}-31}{36}\right)$$

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.

$$18x^{2}+31x-40=0$$

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.

$$x=\frac{-31±\sqrt{31^{2}-4\times 18\left(-40\right)}}{2\times 18}$$

31 kvadratini chiqarish.

$$x=\frac{-31±\sqrt{961-4\times 18\left(-40\right)}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$x=\frac{-31±\sqrt{961-72\left(-40\right)}}{2\times 18}$$

-72 ni -40 marotabaga ko'paytirish.

$$x=\frac{-31±\sqrt{961+2880}}{2\times 18}$$

961 ni 2880 ga qo'shish.

$$x=\frac{-31±\sqrt{3841}}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{-31±\sqrt{3841}}{36}$$

x=\frac{-31±\sqrt{3841}}{36} tenglamasini yeching, bunda ± musbat. -31 ni \sqrt{3841} ga qo'shish.

$$x=\frac{\sqrt{3841}-31}{36}$$

x=\frac{-31±\sqrt{3841}}{36} tenglamasini yeching, bunda ± manfiy. -31 dan \sqrt{3841} ni ayirish.

$$x=\frac{-\sqrt{3841}-31}{36}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-31+\sqrt{3841}}{36} ga va x_{2} uchun \frac{-31-\sqrt{3841}}{36} ga bo‘ling.

$$18x^{2}+31x-40=18\left(x-\frac{\sqrt{3841}-31}{36}\right)\left(x-\frac{-\sqrt{3841}-31}{36}\right)$$

Baholash

$$18x^{2}+31x-40$$