32z^2+3z-40 eching

$$32 z ^ { 2 } + 3 z - 40$$

Omil

$$32\left(z-\frac{-\sqrt{5129}-3}{64}\right)\left(z-\frac{\sqrt{5129}-3}{64}\right)$$

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.

$$32z^{2}+3z-40=0$$

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.

$$z=\frac{-3±\sqrt{3^{2}-4\times 32\left(-40\right)}}{2\times 32}$$

3 kvadratini chiqarish.

$$z=\frac{-3±\sqrt{9-4\times 32\left(-40\right)}}{2\times 32}$$

-4 ni 32 marotabaga ko'paytirish.

$$z=\frac{-3±\sqrt{9-128\left(-40\right)}}{2\times 32}$$

-128 ni -40 marotabaga ko'paytirish.

$$z=\frac{-3±\sqrt{9+5120}}{2\times 32}$$

9 ni 5120 ga qo'shish.

$$z=\frac{-3±\sqrt{5129}}{2\times 32}$$

2 ni 32 marotabaga ko'paytirish.

$$z=\frac{-3±\sqrt{5129}}{64}$$

z=\frac{-3±\sqrt{5129}}{64} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{5129} ga qo'shish.

$$z=\frac{\sqrt{5129}-3}{64}$$

z=\frac{-3±\sqrt{5129}}{64} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{5129} ni ayirish.

$$z=\frac{-\sqrt{5129}-3}{64}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-3+\sqrt{5129}}{64} ga va x_{2} uchun \frac{-3-\sqrt{5129}}{64} ga bo‘ling.

$$32z^{2}+3z-40=32\left(z-\frac{\sqrt{5129}-3}{64}\right)\left(z-\frac{-\sqrt{5129}-3}{64}\right)$$

Baholash

$$32z^{2}+3z-40$$