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x^{2}+13x+58+2x=8
Me tāpiri te 2x ki ngā taha e rua.
x^{2}+15x+58=8
Pahekotia te 13x me 2x, ka 15x.
x^{2}+15x+58-8=0
Tangohia te 8 mai i ngā taha e rua.
x^{2}+15x+50=0
Tangohia te 8 i te 58, ka 50.
a+b=15 ab=50
Hei whakaoti i te whārite, whakatauwehea te x^{2}+15x+50 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.
1,50 2,25 5,10
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 50.
1+50=51 2+25=27 5+10=15
Tātaihia te tapeke mō ia takirua.
a=5 b=10
Ko te otinga te takirua ka hoatu i te tapeke 15.
\left(x+5\right)\left(x+10\right)
Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.
x=-5 x=-10
Hei kimi otinga whārite, me whakaoti te x+5=0 me te x+10=0.
x^{2}+13x+58+2x=8
Me tāpiri te 2x ki ngā taha e rua.
x^{2}+15x+58=8
Pahekotia te 13x me 2x, ka 15x.
x^{2}+15x+58-8=0
Tangohia te 8 mai i ngā taha e rua.
x^{2}+15x+50=0
Tangohia te 8 i te 58, ka 50.
a+b=15 ab=1\times 50=50
Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx+50. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,50 2,25 5,10
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 50.
1+50=51 2+25=27 5+10=15
Tātaihia te tapeke mō ia takirua.
a=5 b=10
Ko te otinga te takirua ka hoatu i te tapeke 15.
\left(x^{2}+5x\right)+\left(10x+50\right)
Tuhia anō te x^{2}+15x+50 hei \left(x^{2}+5x\right)+\left(10x+50\right).
x\left(x+5\right)+10\left(x+5\right)
Tauwehea te x i te tuatahi me te 10 i te rōpū tuarua.
\left(x+5\right)\left(x+10\right)
Whakatauwehea atu te kīanga pātahi x+5 mā te whakamahi i te āhuatanga tātai tohatoha.
x=-5 x=-10
Hei kimi otinga whārite, me whakaoti te x+5=0 me te x+10=0.
x^{2}+13x+58+2x=8
Me tāpiri te 2x ki ngā taha e rua.
x^{2}+15x+58=8
Pahekotia te 13x me 2x, ka 15x.
x^{2}+15x+58-8=0
Tangohia te 8 mai i ngā taha e rua.
x^{2}+15x+50=0
Tangohia te 8 i te 58, ka 50.
x=\frac{-15±\sqrt{15^{2}-4\times 50}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 15 mō b, me 50 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-15±\sqrt{225-4\times 50}}{2}
Pūrua 15.
x=\frac{-15±\sqrt{225-200}}{2}
Whakareatia -4 ki te 50.
x=\frac{-15±\sqrt{25}}{2}
Tāpiri 225 ki te -200.
x=\frac{-15±5}{2}
Tuhia te pūtakerua o te 25.
x=-\frac{10}{2}
Nā, me whakaoti te whārite x=\frac{-15±5}{2} ina he tāpiri te ±. Tāpiri -15 ki te 5.
x=-5
Whakawehe -10 ki te 2.
x=-\frac{20}{2}
Nā, me whakaoti te whārite x=\frac{-15±5}{2} ina he tango te ±. Tango 5 mai i -15.
x=-10
Whakawehe -20 ki te 2.
x=-5 x=-10
Kua oti te whārite te whakatau.
x^{2}+13x+58+2x=8
Me tāpiri te 2x ki ngā taha e rua.
x^{2}+15x+58=8
Pahekotia te 13x me 2x, ka 15x.
x^{2}+15x=8-58
Tangohia te 58 mai i ngā taha e rua.
x^{2}+15x=-50
Tangohia te 58 i te 8, ka -50.
x^{2}+15x+\left(\frac{15}{2}\right)^{2}=-50+\left(\frac{15}{2}\right)^{2}
Whakawehea te 15, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{15}{2}. Nā, tāpiria te pūrua o te \frac{15}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}+15x+\frac{225}{4}=-50+\frac{225}{4}
Pūruatia \frac{15}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.
x^{2}+15x+\frac{225}{4}=\frac{25}{4}
Tāpiri -50 ki te \frac{225}{4}.
\left(x+\frac{15}{2}\right)^{2}=\frac{25}{4}
Tauwehea x^{2}+15x+\frac{225}{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{15}{2}\right)^{2}}=\sqrt{\frac{25}{4}}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x+\frac{15}{2}=\frac{5}{2} x+\frac{15}{2}=-\frac{5}{2}
Whakarūnātia.
x=-5 x=-10
Me tango \frac{15}{2} mai i ngā taha e rua o te whārite.