x^2-74x^2+5+x-1 eching

$$x ^ { 2 } - 74 x ^ { 2 } + 5 + x - 1$$

Baholash

$$4+x-73x^{2}$$

Yechim qadamlari

-73x^{2} ni olish uchun x^{2} va -74x^{2} ni birlashtirish.

$$-73x^{2}+5+x-1$$

4 olish uchun 5 dan 1 ni ayirish.

$$-73x^{2}+4+x$$

Omil

$$-73\left(x-\frac{1-\sqrt{1169}}{146}\right)\left(x-\frac{\sqrt{1169}+1}{146}\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

-73x^{2} ni olish uchun x^{2} va -74x^{2} ni birlashtirish.

$$factor(-73x^{2}+5+x-1)$$

4 olish uchun 5 dan 1 ni ayirish.

$$factor(-73x^{2}+4+x)$$

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.

$$-73x^{2}+x+4=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-73\right)\times 4}}{2\left(-73\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-73\right)\times 4}}{2\left(-73\right)}$$

-4 ni -73 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+292\times 4}}{2\left(-73\right)}$$

292 ni 4 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+1168}}{2\left(-73\right)}$$

1 ni 1168 ga qo'shish.

$$x=\frac{-1±\sqrt{1169}}{2\left(-73\right)}$$

2 ni -73 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1169}}{-146}$$

x=\frac{-1±\sqrt{1169}}{-146} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{1169} ga qo'shish.

$$x=\frac{\sqrt{1169}-1}{-146}$$

-1+\sqrt{1169} ni -146 ga bo'lish.

$$x=\frac{1-\sqrt{1169}}{146}$$

x=\frac{-1±\sqrt{1169}}{-146} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{1169} ni ayirish.

$$x=\frac{-\sqrt{1169}-1}{-146}$$

-1-\sqrt{1169} ni -146 ga bo'lish.

$$x=\frac{\sqrt{1169}+1}{146}$$

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{1169}}{146} ga va x_{2} uchun \frac{1+\sqrt{1169}}{146} ga bo‘ling.

$$-73x^{2}+x+4=-73\left(x-\frac{1-\sqrt{1169}}{146}\right)\left(x-\frac{\sqrt{1169}+1}{146}\right)$$