272+60x-18x^2 eching

$$272+60x-18 { x }^{ 2 }$$

Omil

$$-18\left(x-\frac{5-\sqrt{161}}{3}\right)\left(x-\frac{\sqrt{161}+5}{3}\right)$$

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.

$$-18x^{2}+60x+272=0$$

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.

$$x=\frac{-60±\sqrt{60^{2}-4\left(-18\right)\times 272}}{2\left(-18\right)}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\left(-18\right)\times 272}}{2\left(-18\right)}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+72\times 272}}{2\left(-18\right)}$$

72 ni 272 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+19584}}{2\left(-18\right)}$$

3600 ni 19584 ga qo'shish.

$$x=\frac{-60±\sqrt{23184}}{2\left(-18\right)}$$

23184 ning kvadrat ildizini chiqarish.

$$x=\frac{-60±12\sqrt{161}}{2\left(-18\right)}$$

2 ni -18 marotabaga ko'paytirish.

$$x=\frac{-60±12\sqrt{161}}{-36}$$

x=\frac{-60±12\sqrt{161}}{-36} tenglamasini yeching, bunda ± musbat. -60 ni 12\sqrt{161} ga qo'shish.

$$x=\frac{12\sqrt{161}-60}{-36}$$

-60+12\sqrt{161} ni -36 ga bo'lish.

$$x=\frac{5-\sqrt{161}}{3}$$

x=\frac{-60±12\sqrt{161}}{-36} tenglamasini yeching, bunda ± manfiy. -60 dan 12\sqrt{161} ni ayirish.

$$x=\frac{-12\sqrt{161}-60}{-36}$$

-60-12\sqrt{161} ni -36 ga bo'lish.

$$x=\frac{\sqrt{161}+5}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5-\sqrt{161}}{3} ga va x_{2} uchun \frac{5+\sqrt{161}}{3} ga bo‘ling.

$$-18x^{2}+60x+272=-18\left(x-\frac{5-\sqrt{161}}{3}\right)\left(x-\frac{\sqrt{161}+5}{3}\right)$$

Baholash

$$272+60x-18x^{2}$$