Tīpoka ki ngā ihirangi matua
Whakaoti mō t
Tick mark Image

Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

t\left(t+480\right)=100t+100t+48000
Tē taea kia ōrite te tāupe t ki tētahi o ngā uara -480,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 100t\left(t+480\right), arā, te tauraro pātahi he tino iti rawa te kitea o 100,t+480,t.
t^{2}+480t=100t+100t+48000
Whakamahia te āhuatanga tohatoha hei whakarea te t ki te t+480.
t^{2}+480t=200t+48000
Pahekotia te 100t me 100t, ka 200t.
t^{2}+480t-200t=48000
Tangohia te 200t mai i ngā taha e rua.
t^{2}+280t=48000
Pahekotia te 480t me -200t, ka 280t.
t^{2}+280t-48000=0
Tangohia te 48000 mai i ngā taha e rua.
t=\frac{-280±\sqrt{280^{2}-4\left(-48000\right)}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 280 mō b, me -48000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
t=\frac{-280±\sqrt{78400-4\left(-48000\right)}}{2}
Pūrua 280.
t=\frac{-280±\sqrt{78400+192000}}{2}
Whakareatia -4 ki te -48000.
t=\frac{-280±\sqrt{270400}}{2}
Tāpiri 78400 ki te 192000.
t=\frac{-280±520}{2}
Tuhia te pūtakerua o te 270400.
t=\frac{240}{2}
Nā, me whakaoti te whārite t=\frac{-280±520}{2} ina he tāpiri te ±. Tāpiri -280 ki te 520.
t=120
Whakawehe 240 ki te 2.
t=-\frac{800}{2}
Nā, me whakaoti te whārite t=\frac{-280±520}{2} ina he tango te ±. Tango 520 mai i -280.
t=-400
Whakawehe -800 ki te 2.
t=120 t=-400
Kua oti te whārite te whakatau.
t\left(t+480\right)=100t+100t+48000
Tē taea kia ōrite te tāupe t ki tētahi o ngā uara -480,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 100t\left(t+480\right), arā, te tauraro pātahi he tino iti rawa te kitea o 100,t+480,t.
t^{2}+480t=100t+100t+48000
Whakamahia te āhuatanga tohatoha hei whakarea te t ki te t+480.
t^{2}+480t=200t+48000
Pahekotia te 100t me 100t, ka 200t.
t^{2}+480t-200t=48000
Tangohia te 200t mai i ngā taha e rua.
t^{2}+280t=48000
Pahekotia te 480t me -200t, ka 280t.
t^{2}+280t+140^{2}=48000+140^{2}
Whakawehea te 280, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 140. Nā, tāpiria te pūrua o te 140 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
t^{2}+280t+19600=48000+19600
Pūrua 140.
t^{2}+280t+19600=67600
Tāpiri 48000 ki te 19600.
\left(t+140\right)^{2}=67600
Tauwehea t^{2}+280t+19600. 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}.
\sqrt{\left(t+140\right)^{2}}=\sqrt{67600}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
t+140=260 t+140=-260
Whakarūnātia.
t=120 t=-400
Me tango 140 mai i ngā taha e rua o te whārite.