h(t)=-49t^2+307t+115 eching

$$h ( t ) = - 49 t ^ { 2 } + 307 t + 115$$

Omil

$$-49\left(t-\frac{307-\sqrt{116789}}{98}\right)\left(t-\frac{\sqrt{116789}+307}{98}\right)$$

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.

$$-49t^{2}+307t+115=0$$

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.

$$t=\frac{-307±\sqrt{307^{2}-4\left(-49\right)\times 115}}{2\left(-49\right)}$$

307 kvadratini chiqarish.

$$t=\frac{-307±\sqrt{94249-4\left(-49\right)\times 115}}{2\left(-49\right)}$$

-4 ni -49 marotabaga ko'paytirish.

$$t=\frac{-307±\sqrt{94249+196\times 115}}{2\left(-49\right)}$$

196 ni 115 marotabaga ko'paytirish.

$$t=\frac{-307±\sqrt{94249+22540}}{2\left(-49\right)}$$

94249 ni 22540 ga qo'shish.

$$t=\frac{-307±\sqrt{116789}}{2\left(-49\right)}$$

2 ni -49 marotabaga ko'paytirish.

$$t=\frac{-307±\sqrt{116789}}{-98}$$

t=\frac{-307±\sqrt{116789}}{-98} tenglamasini yeching, bunda ± musbat. -307 ni \sqrt{116789} ga qo'shish.

$$t=\frac{\sqrt{116789}-307}{-98}$$

-307+\sqrt{116789} ni -98 ga bo'lish.

$$t=\frac{307-\sqrt{116789}}{98}$$

t=\frac{-307±\sqrt{116789}}{-98} tenglamasini yeching, bunda ± manfiy. -307 dan \sqrt{116789} ni ayirish.

$$t=\frac{-\sqrt{116789}-307}{-98}$$

-307-\sqrt{116789} ni -98 ga bo'lish.

$$t=\frac{\sqrt{116789}+307}{98}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{307-\sqrt{116789}}{98} ga va x_{2} uchun \frac{307+\sqrt{116789}}{98} ga bo‘ling.

$$-49t^{2}+307t+115=-49\left(t-\frac{307-\sqrt{116789}}{98}\right)\left(t-\frac{\sqrt{116789}+307}{98}\right)$$

Baholash

$$115+307t-49t^{2}$$