9x^2-200x-455 eching

$$9 { x }^{ 2 } -200x-455$$

Omil

$$9\left(x-\frac{100-\sqrt{14095}}{9}\right)\left(x-\frac{\sqrt{14095}+100}{9}\right)$$

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.

$$9x^{2}-200x-455=0$$

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.

$$x=\frac{-\left(-200\right)±\sqrt{\left(-200\right)^{2}-4\times 9\left(-455\right)}}{2\times 9}$$

-200 kvadratini chiqarish.

$$x=\frac{-\left(-200\right)±\sqrt{40000-4\times 9\left(-455\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-200\right)±\sqrt{40000-36\left(-455\right)}}{2\times 9}$$

-36 ni -455 marotabaga ko'paytirish.

$$x=\frac{-\left(-200\right)±\sqrt{40000+16380}}{2\times 9}$$

40000 ni 16380 ga qo'shish.

$$x=\frac{-\left(-200\right)±\sqrt{56380}}{2\times 9}$$

56380 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-200\right)±2\sqrt{14095}}{2\times 9}$$

-200 ning teskarisi 200 ga teng.

$$x=\frac{200±2\sqrt{14095}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{200±2\sqrt{14095}}{18}$$

x=\frac{200±2\sqrt{14095}}{18} tenglamasini yeching, bunda ± musbat. 200 ni 2\sqrt{14095} ga qo'shish.

$$x=\frac{2\sqrt{14095}+200}{18}$$

200+2\sqrt{14095} ni 18 ga bo'lish.

$$x=\frac{\sqrt{14095}+100}{9}$$

x=\frac{200±2\sqrt{14095}}{18} tenglamasini yeching, bunda ± manfiy. 200 dan 2\sqrt{14095} ni ayirish.

$$x=\frac{200-2\sqrt{14095}}{18}$$

200-2\sqrt{14095} ni 18 ga bo'lish.

$$x=\frac{100-\sqrt{14095}}{9}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{100+\sqrt{14095}}{9} ga va x_{2} uchun \frac{100-\sqrt{14095}}{9} ga bo‘ling.

$$9x^{2}-200x-455=9\left(x-\frac{\sqrt{14095}+100}{9}\right)\left(x-\frac{100-\sqrt{14095}}{9}\right)$$

Baholash

$$9x^{2}-200x-455$$