-16t^2+88t+4 eching

$$- 16 t ^ { 2 } + 88 t + 4$$

Omil

$$-16\left(t-\frac{11-5\sqrt{5}}{4}\right)\left(t-\frac{5\sqrt{5}+11}{4}\right)$$

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.

$$-16t^{2}+88t+4=0$$

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.

$$t=\frac{-88±\sqrt{88^{2}-4\left(-16\right)\times 4}}{2\left(-16\right)}$$

88 kvadratini chiqarish.

$$t=\frac{-88±\sqrt{7744-4\left(-16\right)\times 4}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{-88±\sqrt{7744+64\times 4}}{2\left(-16\right)}$$

64 ni 4 marotabaga ko'paytirish.

$$t=\frac{-88±\sqrt{7744+256}}{2\left(-16\right)}$$

7744 ni 256 ga qo'shish.

$$t=\frac{-88±\sqrt{8000}}{2\left(-16\right)}$$

8000 ning kvadrat ildizini chiqarish.

$$t=\frac{-88±40\sqrt{5}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{-88±40\sqrt{5}}{-32}$$

t=\frac{-88±40\sqrt{5}}{-32} tenglamasini yeching, bunda ± musbat. -88 ni 40\sqrt{5} ga qo'shish.

$$t=\frac{40\sqrt{5}-88}{-32}$$

-88+40\sqrt{5} ni -32 ga bo'lish.

$$t=\frac{11-5\sqrt{5}}{4}$$

t=\frac{-88±40\sqrt{5}}{-32} tenglamasini yeching, bunda ± manfiy. -88 dan 40\sqrt{5} ni ayirish.

$$t=\frac{-40\sqrt{5}-88}{-32}$$

-88-40\sqrt{5} ni -32 ga bo'lish.

$$t=\frac{5\sqrt{5}+11}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{11-5\sqrt{5}}{4} ga va x_{2} uchun \frac{11+5\sqrt{5}}{4} ga bo‘ling.

$$-16t^{2}+88t+4=-16\left(t-\frac{11-5\sqrt{5}}{4}\right)\left(t-\frac{5\sqrt{5}+11}{4}\right)$$

Baholash

$$4+88t-16t^{2}$$