Whakaoti i te -4.9t^2+98t+100=0

$$- 4.9 t ^ { 2 } + 98 t + 100 = 0$$

Whakaoti mō t

$$t=\frac{10\sqrt{59}}{7}+10\approx 20.973065354$$

$$t=-\frac{10\sqrt{59}}{7}+10\approx -0.973065354$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-4.9t^{2}+98t+100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4.9 mō a, 98 mō b, me 100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-98±\sqrt{98^{2}-4\left(-4.9\right)\times 100}}{2\left(-4.9\right)}$$

Pūrua 98.

$$t=\frac{-98±\sqrt{9604-4\left(-4.9\right)\times 100}}{2\left(-4.9\right)}$$

Whakareatia -4 ki te -4.9.

$$t=\frac{-98±\sqrt{9604+19.6\times 100}}{2\left(-4.9\right)}$$

Whakareatia 19.6 ki te 100.

$$t=\frac{-98±\sqrt{9604+1960}}{2\left(-4.9\right)}$$

Tāpiri 9604 ki te 1960.

$$t=\frac{-98±\sqrt{11564}}{2\left(-4.9\right)}$$

Tuhia te pūtakerua o te 11564.

$$t=\frac{-98±14\sqrt{59}}{2\left(-4.9\right)}$$

Whakareatia 2 ki te -4.9.

$$t=\frac{-98±14\sqrt{59}}{-9.8}$$

Nā, me whakaoti te whārite t=\frac{-98±14\sqrt{59}}{-9.8} ina he tāpiri te ±. Tāpiri -98 ki te 14\sqrt{59}.

$$t=\frac{14\sqrt{59}-98}{-9.8}$$

Whakawehe -98+14\sqrt{59} ki te -9.8 mā te whakarea -98+14\sqrt{59} ki te tau huripoki o -9.8.

$$t=-\frac{10\sqrt{59}}{7}+10$$

Nā, me whakaoti te whārite t=\frac{-98±14\sqrt{59}}{-9.8} ina he tango te ±. Tango 14\sqrt{59} mai i -98.

$$t=\frac{-14\sqrt{59}-98}{-9.8}$$

Whakawehe -98-14\sqrt{59} ki te -9.8 mā te whakarea -98-14\sqrt{59} ki te tau huripoki o -9.8.

$$t=\frac{10\sqrt{59}}{7}+10$$

Kua oti te whārite te whakatau.

$$t=-\frac{10\sqrt{59}}{7}+10 t=\frac{10\sqrt{59}}{7}+10$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-4.9t^{2}+98t+100=0$$

Me tango 100 mai i ngā taha e rua o te whārite.

$$-4.9t^{2}+98t+100-100=-100$$

Mā te tango i te 100 i a ia ake anō ka toe ko te 0.

$$-4.9t^{2}+98t=-100$$

Whakawehea ngā taha e rua o te whārite ki te -4.9, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-4.9t^{2}+98t}{-4.9}=-\frac{100}{-4.9}$$

Mā te whakawehe ki te -4.9 ka wetekia te whakareanga ki te -4.9.

$$t^{2}+\frac{98}{-4.9}t=-\frac{100}{-4.9}$$

Whakawehe 98 ki te -4.9 mā te whakarea 98 ki te tau huripoki o -4.9.

$$t^{2}-20t=-\frac{100}{-4.9}$$

Whakawehe -100 ki te -4.9 mā te whakarea -100 ki te tau huripoki o -4.9.

$$t^{2}-20t=\frac{1000}{49}$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-20t+\left(-10\right)^{2}=\frac{1000}{49}+\left(-10\right)^{2}$$

Pūrua -10.

$$t^{2}-20t+100=\frac{1000}{49}+100$$

Tāpiri \frac{1000}{49} ki te 100.

$$t^{2}-20t+100=\frac{5900}{49}$$

Tauwehea t^{2}-20t+100. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(t-10\right)^{2}=\frac{5900}{49}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(t-10\right)^{2}}=\sqrt{\frac{5900}{49}}$$

Whakarūnātia.

$$t-10=\frac{10\sqrt{59}}{7} t-10=-\frac{10\sqrt{59}}{7}$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$t=\frac{10\sqrt{59}}{7}+10 t=-\frac{10\sqrt{59}}{7}+10$$