9a^2+42a-49 eching

$$9 a ^ { 2 } + 42 a - 49$$

Omil

$$9\left(a-\frac{-7\sqrt{2}-7}{3}\right)\left(a-\frac{7\sqrt{2}-7}{3}\right)$$

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.

$$9a^{2}+42a-49=0$$

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.

$$a=\frac{-42±\sqrt{42^{2}-4\times 9\left(-49\right)}}{2\times 9}$$

42 kvadratini chiqarish.

$$a=\frac{-42±\sqrt{1764-4\times 9\left(-49\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$a=\frac{-42±\sqrt{1764-36\left(-49\right)}}{2\times 9}$$

-36 ni -49 marotabaga ko'paytirish.

$$a=\frac{-42±\sqrt{1764+1764}}{2\times 9}$$

1764 ni 1764 ga qo'shish.

$$a=\frac{-42±\sqrt{3528}}{2\times 9}$$

3528 ning kvadrat ildizini chiqarish.

$$a=\frac{-42±42\sqrt{2}}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$a=\frac{-42±42\sqrt{2}}{18}$$

a=\frac{-42±42\sqrt{2}}{18} tenglamasini yeching, bunda ± musbat. -42 ni 42\sqrt{2} ga qo'shish.

$$a=\frac{42\sqrt{2}-42}{18}$$

-42+42\sqrt{2} ni 18 ga bo'lish.

$$a=\frac{7\sqrt{2}-7}{3}$$

a=\frac{-42±42\sqrt{2}}{18} tenglamasini yeching, bunda ± manfiy. -42 dan 42\sqrt{2} ni ayirish.

$$a=\frac{-42\sqrt{2}-42}{18}$$

-42-42\sqrt{2} ni 18 ga bo'lish.

$$a=\frac{-7\sqrt{2}-7}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-7+7\sqrt{2}}{3} ga va x_{2} uchun \frac{-7-7\sqrt{2}}{3} ga bo‘ling.

$$9a^{2}+42a-49=9\left(a-\frac{7\sqrt{2}-7}{3}\right)\left(a-\frac{-7\sqrt{2}-7}{3}\right)$$

Baholash

$$9a^{2}+42a-49$$