49x^2+2x-15 eching

$$49 { x }^{ 2 } +2x-15$$

Omil

$$49\left(x-\frac{-4\sqrt{46}-1}{49}\right)\left(x-\frac{4\sqrt{46}-1}{49}\right)$$

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.

$$49x^{2}+2x-15=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 49\left(-15\right)}}{2\times 49}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 49\left(-15\right)}}{2\times 49}$$

-4 ni 49 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-196\left(-15\right)}}{2\times 49}$$

-196 ni -15 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+2940}}{2\times 49}$$

4 ni 2940 ga qo'shish.

$$x=\frac{-2±\sqrt{2944}}{2\times 49}$$

2944 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±8\sqrt{46}}{2\times 49}$$

2 ni 49 marotabaga ko'paytirish.

$$x=\frac{-2±8\sqrt{46}}{98}$$

x=\frac{-2±8\sqrt{46}}{98} tenglamasini yeching, bunda ± musbat. -2 ni 8\sqrt{46} ga qo'shish.

$$x=\frac{8\sqrt{46}-2}{98}$$

-2+8\sqrt{46} ni 98 ga bo'lish.

$$x=\frac{4\sqrt{46}-1}{49}$$

x=\frac{-2±8\sqrt{46}}{98} tenglamasini yeching, bunda ± manfiy. -2 dan 8\sqrt{46} ni ayirish.

$$x=\frac{-8\sqrt{46}-2}{98}$$

-2-8\sqrt{46} ni 98 ga bo'lish.

$$x=\frac{-4\sqrt{46}-1}{49}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-1+4\sqrt{46}}{49} ga va x_{2} uchun \frac{-1-4\sqrt{46}}{49} ga bo‘ling.

$$49x^{2}+2x-15=49\left(x-\frac{4\sqrt{46}-1}{49}\right)\left(x-\frac{-4\sqrt{46}-1}{49}\right)$$

Baholash

$$49x^{2}+2x-15$$