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x^{2}+7x+15-5=0
Tangohia te 5 mai i ngā taha e rua.
x^{2}+7x+10=0
Tangohia te 5 i te 15, ka 10.
a+b=7 ab=10
Hei whakaoti i te whārite, whakatauwehea te x^{2}+7x+10 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,10 2,5
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 10.
1+10=11 2+5=7
Tātaihia te tapeke mō ia takirua.
a=2 b=5
Ko te otinga te takirua ka hoatu i te tapeke 7.
\left(x+2\right)\left(x+5\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=-2 x=-5
Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+5=0.
x^{2}+7x+15-5=0
Tangohia te 5 mai i ngā taha e rua.
x^{2}+7x+10=0
Tangohia te 5 i te 15, ka 10.
a+b=7 ab=1\times 10=10
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,10 2,5
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 10.
1+10=11 2+5=7
Tātaihia te tapeke mō ia takirua.
a=2 b=5
Ko te otinga te takirua ka hoatu i te tapeke 7.
\left(x^{2}+2x\right)+\left(5x+10\right)
Tuhia anō te x^{2}+7x+10 hei \left(x^{2}+2x\right)+\left(5x+10\right).
x\left(x+2\right)+5\left(x+2\right)
Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.
\left(x+2\right)\left(x+5\right)
Whakatauwehea atu te kīanga pātahi x+2 mā te whakamahi i te āhuatanga tātai tohatoha.
x=-2 x=-5
Hei kimi otinga whārite, me whakaoti te x+2=0 me te x+5=0.
x^{2}+7x+15=5
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.
x^{2}+7x+15-5=5-5
Me tango 5 mai i ngā taha e rua o te whārite.
x^{2}+7x+15-5=0
Mā te tango i te 5 i a ia ake anō ka toe ko te 0.
x^{2}+7x+10=0
Tango 5 mai i 15.
x=\frac{-7±\sqrt{7^{2}-4\times 10}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-7±\sqrt{49-4\times 10}}{2}
Pūrua 7.
x=\frac{-7±\sqrt{49-40}}{2}
Whakareatia -4 ki te 10.
x=\frac{-7±\sqrt{9}}{2}
Tāpiri 49 ki te -40.
x=\frac{-7±3}{2}
Tuhia te pūtakerua o te 9.
x=-\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{-7±3}{2} ina he tāpiri te ±. Tāpiri -7 ki te 3.
x=-2
Whakawehe -4 ki te 2.
x=-\frac{10}{2}
Nā, me whakaoti te whārite x=\frac{-7±3}{2} ina he tango te ±. Tango 3 mai i -7.
x=-5
Whakawehe -10 ki te 2.
x=-2 x=-5
Kua oti te whārite te whakatau.
x^{2}+7x+15=5
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.
x^{2}+7x+15-15=5-15
Me tango 15 mai i ngā taha e rua o te whārite.
x^{2}+7x=5-15
Mā te tango i te 15 i a ia ake anō ka toe ko te 0.
x^{2}+7x=-10
Tango 15 mai i 5.
x^{2}+7x+\left(\frac{7}{2}\right)^{2}=-10+\left(\frac{7}{2}\right)^{2}
Whakawehea te 7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{2}. Nā, tāpiria te pūrua o te \frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+7x+\frac{49}{4}=-10+\frac{49}{4}
Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+7x+\frac{49}{4}=\frac{9}{4}
Tāpiri -10 ki te \frac{49}{4}.
\left(x+\frac{7}{2}\right)^{2}=\frac{9}{4}
Tauwehea x^{2}+7x+\frac{49}{4}. 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{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{7}{2}=\frac{3}{2} x+\frac{7}{2}=-\frac{3}{2}
Whakarūnātia.
x=-2 x=-5
Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.