Whakaoti i te 190=(x+9)(x)

$$190=(x+9)(x)$$

Whakaoti mō x

$$x=-19$$

$$x=10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te x.

$$190=x^{2}+9x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+9x=190$$

Tangohia te 190 mai i ngā taha e rua.

$$x^{2}+9x-190=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 9 mō b, me -190 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}-4\left(-190\right)}}{2}$$

Pūrua 9.

$$x=\frac{-9±\sqrt{81-4\left(-190\right)}}{2}$$

Whakareatia -4 ki te -190.

$$x=\frac{-9±\sqrt{81+760}}{2}$$

Tāpiri 81 ki te 760.

$$x=\frac{-9±\sqrt{841}}{2}$$

Tuhia te pūtakerua o te 841.

$$x=\frac{-9±29}{2}$$

Nā, me whakaoti te whārite x=\frac{-9±29}{2} ina he tāpiri te ±. Tāpiri -9 ki te 29.

$$x=\frac{20}{2}$$

Whakawehe 20 ki te 2.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{-9±29}{2} ina he tango te ±. Tango 29 mai i -9.

$$x=-\frac{38}{2}$$

Whakawehe -38 ki te 2.

$$x=-19$$

Kua oti te whārite te whakatau.

$$x=10 x=-19$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+9 ki te x.

$$190=x^{2}+9x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}+9x=190$$

Whakawehea te 9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{9}{2}. Nā, tāpiria te pūrua o te \frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=190+\left(\frac{9}{2}\right)^{2}$$

Pūruatia \frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+9x+\frac{81}{4}=190+\frac{81}{4}$$

Tāpiri 190 ki te \frac{81}{4}.

$$x^{2}+9x+\frac{81}{4}=\frac{841}{4}$$

Tauwehea x^{2}+9x+\frac{81}{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}.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{841}{4}$$

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

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{841}{4}}$$

Whakarūnātia.

$$x+\frac{9}{2}=\frac{29}{2} x+\frac{9}{2}=-\frac{29}{2}$$

Me tango \frac{9}{2} mai i ngā taha e rua o te whārite.

$$x=10 x=-19$$