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28x^{2}+41x+15=2
Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+3 ki te 7x+5 ka whakakotahi i ngā kupu rite.
28x^{2}+41x+15-2=0
Tangohia te 2 mai i ngā taha e rua.
28x^{2}+41x+13=0
Tangohia te 2 i te 15, ka 13.
x=\frac{-41±\sqrt{41^{2}-4\times 28\times 13}}{2\times 28}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 28 mō a, 41 mō b, me 13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-41±\sqrt{1681-4\times 28\times 13}}{2\times 28}
Pūrua 41.
x=\frac{-41±\sqrt{1681-112\times 13}}{2\times 28}
Whakareatia -4 ki te 28.
x=\frac{-41±\sqrt{1681-1456}}{2\times 28}
Whakareatia -112 ki te 13.
x=\frac{-41±\sqrt{225}}{2\times 28}
Tāpiri 1681 ki te -1456.
x=\frac{-41±15}{2\times 28}
Tuhia te pūtakerua o te 225.
x=\frac{-41±15}{56}
Whakareatia 2 ki te 28.
x=-\frac{26}{56}
Nā, me whakaoti te whārite x=\frac{-41±15}{56} ina he tāpiri te ±. Tāpiri -41 ki te 15.
x=-\frac{13}{28}
Whakahekea te hautanga \frac{-26}{56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
x=-\frac{56}{56}
Nā, me whakaoti te whārite x=\frac{-41±15}{56} ina he tango te ±. Tango 15 mai i -41.
x=-1
Whakawehe -56 ki te 56.
x=-\frac{13}{28} x=-1
Kua oti te whārite te whakatau.
28x^{2}+41x+15=2
Whakamahia te āhuatanga tuaritanga hei whakarea te 4x+3 ki te 7x+5 ka whakakotahi i ngā kupu rite.
28x^{2}+41x=2-15
Tangohia te 15 mai i ngā taha e rua.
28x^{2}+41x=-13
Tangohia te 15 i te 2, ka -13.
\frac{28x^{2}+41x}{28}=-\frac{13}{28}
Whakawehea ngā taha e rua ki te 28.
x^{2}+\frac{41}{28}x=-\frac{13}{28}
Mā te whakawehe ki te 28 ka wetekia te whakareanga ki te 28.
x^{2}+\frac{41}{28}x+\left(\frac{41}{56}\right)^{2}=-\frac{13}{28}+\left(\frac{41}{56}\right)^{2}
Whakawehea te \frac{41}{28}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{41}{56}. Nā, tāpiria te pūrua o te \frac{41}{56} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+\frac{41}{28}x+\frac{1681}{3136}=-\frac{13}{28}+\frac{1681}{3136}
Pūruatia \frac{41}{56} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+\frac{41}{28}x+\frac{1681}{3136}=\frac{225}{3136}
Tāpiri -\frac{13}{28} ki te \frac{1681}{3136} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
\left(x+\frac{41}{56}\right)^{2}=\frac{225}{3136}
Tauwehea x^{2}+\frac{41}{28}x+\frac{1681}{3136}. 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(x+\frac{41}{56}\right)^{2}}=\sqrt{\frac{225}{3136}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{41}{56}=\frac{15}{56} x+\frac{41}{56}=-\frac{15}{56}
Whakarūnātia.
x=-\frac{13}{28} x=-1
Me tango \frac{41}{56} mai i ngā taha e rua o te whārite.