3x^2-3x-225 eching

$$3 x ^ { 2 } - 3 x - 225$$

Omil

$$3\left(x-\frac{1-\sqrt{301}}{2}\right)\left(x-\frac{\sqrt{301}+1}{2}\right)$$

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.

$$3x^{2}-3x-225=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 3\left(-225\right)}}{2\times 3}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 3\left(-225\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-12\left(-225\right)}}{2\times 3}$$

-12 ni -225 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+2700}}{2\times 3}$$

9 ni 2700 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{2709}}{2\times 3}$$

2709 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±3\sqrt{301}}{2\times 3}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3\sqrt{301}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{3±3\sqrt{301}}{6}$$

x=\frac{3±3\sqrt{301}}{6} tenglamasini yeching, bunda ± musbat. 3 ni 3\sqrt{301} ga qo'shish.

$$x=\frac{3\sqrt{301}+3}{6}$$

3+3\sqrt{301} ni 6 ga bo'lish.

$$x=\frac{\sqrt{301}+1}{2}$$

x=\frac{3±3\sqrt{301}}{6} tenglamasini yeching, bunda ± manfiy. 3 dan 3\sqrt{301} ni ayirish.

$$x=\frac{3-3\sqrt{301}}{6}$$

3-3\sqrt{301} ni 6 ga bo'lish.

$$x=\frac{1-\sqrt{301}}{2}$$

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{301}}{2} ga va x_{2} uchun \frac{1-\sqrt{301}}{2} ga bo‘ling.

$$3x^{2}-3x-225=3\left(x-\frac{\sqrt{301}+1}{2}\right)\left(x-\frac{1-\sqrt{301}}{2}\right)$$

Baholash

$$3\left(x^{2}-x-75\right)$$