Whakaoti i te (x+19)x=8100

$$(x+19)x=8100$$

Whakaoti mō x

$$x=-100$$

$$x=81$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+19 ki te x.

$$x^{2}+19x=8100$$

Tangohia te 8100 mai i ngā taha e rua.

$$x^{2}+19x-8100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 19 mō b, me -8100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-19±\sqrt{19^{2}-4\left(-8100\right)}}{2}$$

Pūrua 19.

$$x=\frac{-19±\sqrt{361-4\left(-8100\right)}}{2}$$

Whakareatia -4 ki te -8100.

$$x=\frac{-19±\sqrt{361+32400}}{2}$$

Tāpiri 361 ki te 32400.

$$x=\frac{-19±\sqrt{32761}}{2}$$

Tuhia te pūtakerua o te 32761.

$$x=\frac{-19±181}{2}$$

Nā, me whakaoti te whārite x=\frac{-19±181}{2} ina he tāpiri te ±. Tāpiri -19 ki te 181.

$$x=\frac{162}{2}$$

Whakawehe 162 ki te 2.

$$x=81$$

Nā, me whakaoti te whārite x=\frac{-19±181}{2} ina he tango te ±. Tango 181 mai i -19.

$$x=-\frac{200}{2}$$

Whakawehe -200 ki te 2.

$$x=-100$$

Kua oti te whārite te whakatau.

$$x=81 x=-100$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+19 ki te x.

$$x^{2}+19x=8100$$

Whakawehea te 19, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{19}{2}. Nā, tāpiria te pūrua o te \frac{19}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+19x+\left(\frac{19}{2}\right)^{2}=8100+\left(\frac{19}{2}\right)^{2}$$

Pūruatia \frac{19}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+19x+\frac{361}{4}=8100+\frac{361}{4}$$

Tāpiri 8100 ki te \frac{361}{4}.

$$x^{2}+19x+\frac{361}{4}=\frac{32761}{4}$$

Tauwehea x^{2}+19x+\frac{361}{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}.

$$\left(x+\frac{19}{2}\right)^{2}=\frac{32761}{4}$$

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

$$\sqrt{\left(x+\frac{19}{2}\right)^{2}}=\sqrt{\frac{32761}{4}}$$

Whakarūnātia.

$$x+\frac{19}{2}=\frac{181}{2} x+\frac{19}{2}=-\frac{181}{2}$$

Me tango \frac{19}{2} mai i ngā taha e rua o te whārite.

$$x=81 x=-100$$