Whakaoti i te 6(6+15)=x(x+5)

$$6(6+15)=x(x+5)$$

Whakaoti mō x

$$x=-14$$

$$x=9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 6 ki te 15, ka 21.

$$6\times 21=x\left(x+5\right)$$

Whakareatia te 6 ki te 21, ka 126.

$$126=x\left(x+5\right)$$

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

$$126=x^{2}+5x$$

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

$$x^{2}+5x=126$$

Tangohia te 126 mai i ngā taha e rua.

$$x^{2}+5x-126=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -126 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-126\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-126\right)}}{2}$$

Whakareatia -4 ki te -126.

$$x=\frac{-5±\sqrt{25+504}}{2}$$

Tāpiri 25 ki te 504.

$$x=\frac{-5±\sqrt{529}}{2}$$

Tuhia te pūtakerua o te 529.

$$x=\frac{-5±23}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±23}{2} ina he tāpiri te ±. Tāpiri -5 ki te 23.

$$x=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{-5±23}{2} ina he tango te ±. Tango 23 mai i -5.

$$x=-\frac{28}{2}$$

Whakawehe -28 ki te 2.

$$x=-14$$

Kua oti te whārite te whakatau.

$$x=9 x=-14$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 6 ki te 15, ka 21.

$$6\times 21=x\left(x+5\right)$$

Whakareatia te 6 ki te 21, ka 126.

$$126=x\left(x+5\right)$$

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

$$126=x^{2}+5x$$

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

$$x^{2}+5x=126$$

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.

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=126+\left(\frac{5}{2}\right)^{2}$$

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

$$x^{2}+5x+\frac{25}{4}=126+\frac{25}{4}$$

Tāpiri 126 ki te \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{529}{4}$$

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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{529}{4}$$

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

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{529}{4}}$$

Whakarūnātia.

$$x+\frac{5}{2}=\frac{23}{2} x+\frac{5}{2}=-\frac{23}{2}$$

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

$$x=9 x=-14$$