x^2+30x-120 eching

$${ x }^{ 2 } +30x-120$$

Omil

$$\left(x-\left(-\sqrt{345}-15\right)\right)\left(x-\left(\sqrt{345}-15\right)\right)$$

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.

$$x^{2}+30x-120=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\left(-120\right)}}{2}$$

30 kvadratini chiqarish.

$$x=\frac{-30±\sqrt{900-4\left(-120\right)}}{2}$$

-4 ni -120 marotabaga ko'paytirish.

$$x=\frac{-30±\sqrt{900+480}}{2}$$

900 ni 480 ga qo'shish.

$$x=\frac{-30±\sqrt{1380}}{2}$$

1380 ning kvadrat ildizini chiqarish.

$$x=\frac{-30±2\sqrt{345}}{2}$$

x=\frac{-30±2\sqrt{345}}{2} tenglamasini yeching, bunda ± musbat. -30 ni 2\sqrt{345} ga qo'shish.

$$x=\frac{2\sqrt{345}-30}{2}$$

-30+2\sqrt{345} ni 2 ga bo'lish.

$$x=\sqrt{345}-15$$

x=\frac{-30±2\sqrt{345}}{2} tenglamasini yeching, bunda ± manfiy. -30 dan 2\sqrt{345} ni ayirish.

$$x=\frac{-2\sqrt{345}-30}{2}$$

-30-2\sqrt{345} ni 2 ga bo'lish.

$$x=-\sqrt{345}-15$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -15+\sqrt{345} ga va x_{2} uchun -15-\sqrt{345} ga bo‘ling.

$$x^{2}+30x-120=\left(x-\left(\sqrt{345}-15\right)\right)\left(x-\left(-\sqrt{345}-15\right)\right)$$

Baholash

$$x^{2}+30x-120$$