5v^2+30v-70 eching

$$5 v ^ { 2 } + 30 v - 70$$

Omil

$$5\left(v-\left(-\sqrt{23}-3\right)\right)\left(v-\left(\sqrt{23}-3\right)\right)$$

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.

$$5v^{2}+30v-70=0$$

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.

$$v=\frac{-30±\sqrt{30^{2}-4\times 5\left(-70\right)}}{2\times 5}$$

30 kvadratini chiqarish.

$$v=\frac{-30±\sqrt{900-4\times 5\left(-70\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$v=\frac{-30±\sqrt{900-20\left(-70\right)}}{2\times 5}$$

-20 ni -70 marotabaga ko'paytirish.

$$v=\frac{-30±\sqrt{900+1400}}{2\times 5}$$

900 ni 1400 ga qo'shish.

$$v=\frac{-30±\sqrt{2300}}{2\times 5}$$

2300 ning kvadrat ildizini chiqarish.

$$v=\frac{-30±10\sqrt{23}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$v=\frac{-30±10\sqrt{23}}{10}$$

v=\frac{-30±10\sqrt{23}}{10} tenglamasini yeching, bunda ± musbat. -30 ni 10\sqrt{23} ga qo'shish.

$$v=\frac{10\sqrt{23}-30}{10}$$

-30+10\sqrt{23} ni 10 ga bo'lish.

$$v=\sqrt{23}-3$$

v=\frac{-30±10\sqrt{23}}{10} tenglamasini yeching, bunda ± manfiy. -30 dan 10\sqrt{23} ni ayirish.

$$v=\frac{-10\sqrt{23}-30}{10}$$

-30-10\sqrt{23} ni 10 ga bo'lish.

$$v=-\sqrt{23}-3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -3+\sqrt{23} ga va x_{2} uchun -3-\sqrt{23} ga bo‘ling.

$$5v^{2}+30v-70=5\left(v-\left(\sqrt{23}-3\right)\right)\left(v-\left(-\sqrt{23}-3\right)\right)$$

Baholash

$$5\left(v^{2}+6v-14\right)$$