Whakaoti i te (x+3)(x-2)=24

$$( x + 3 ) ( x - 2 ) = 24$$

Whakaoti mō x

$$x=-6$$

$$x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}+x-6=24$$

Tangohia te 24 mai i ngā taha e rua.

$$x^{2}+x-6-24=0$$

Tangohia te 24 i te -6, ka -30.

$$x^{2}+x-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-30\right)}}{2}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-30\right)}}{2}$$

Whakareatia -4 ki te -30.

$$x=\frac{-1±\sqrt{1+120}}{2}$$

Tāpiri 1 ki te 120.

$$x=\frac{-1±\sqrt{121}}{2}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-1±11}{2}$$

Nā, me whakaoti te whārite x=\frac{-1±11}{2} ina he tāpiri te ±. Tāpiri -1 ki te 11.

$$x=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{-1±11}{2} ina he tango te ±. Tango 11 mai i -1.

$$x=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=5 x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}+x-6=24$$

Me tāpiri te 6 ki ngā taha e rua.

$$x^{2}+x=24+6$$

Tāpirihia te 24 ki te 6, ka 30.

$$x^{2}+x=30$$

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=30+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=30+\frac{1}{4}$$

Tāpiri 30 ki te \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{121}{4}$$

Tauwehea te x^{2}+x+\frac{1}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{121}{4}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{11}{2} x+\frac{1}{2}=-\frac{11}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=5 x=-6$$