Whakaoti i te (x+5)*x=24

$$( x + 5 ) \cdot x = 24$$

Whakaoti mō x

$$x=-8$$

$$x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+5 ki te x.

$$x^{2}+5x=24$$

Tangohia te 24 mai i ngā taha e rua.

$$x^{2}+5x-24=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -24 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-24\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-24\right)}}{2}$$

Whakareatia -4 ki te -24.

$$x=\frac{-5±\sqrt{25+96}}{2}$$

Tāpiri 25 ki te 96.

$$x=\frac{-5±\sqrt{121}}{2}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-5±11}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{2} ina he tāpiri te ±. Tāpiri -5 ki te 11.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-5±11}{2} ina he tango te ±. Tango 11 mai i -5.

$$x=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=3 x=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x+5 ki te x.

$$x^{2}+5x=24$$

Whakawehea te 5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{2}. Nā, tāpiria te pūrua o te \frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=24+\left(\frac{5}{2}\right)^{2}$$

Pūruatia \frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+5x+\frac{25}{4}=24+\frac{25}{4}$$

Tāpiri 24 ki te \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{121}{4}$$

Tauwehea x^{2}+5x+\frac{25}{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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{121}{4}$$

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

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Whakarūnātia.

$$x+\frac{5}{2}=\frac{11}{2} x+\frac{5}{2}=-\frac{11}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$x=3 x=-8$$