Whakaoti i te 36=x(x-5)

$$36=x(x-5)$$

Whakaoti mō x

$$x=-4$$

$$x=9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$36=x^{2}-5x$$

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

$$x^{2}-5x=36$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}-5x-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -5 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-36\right)}}{2}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$x=\frac{-\left(-5\right)±\sqrt{25+144}}{2}$$

Tāpiri 25 ki te 144.

$$x=\frac{-\left(-5\right)±\sqrt{169}}{2}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-\left(-5\right)±13}{2}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±13}{2}$$

Nā, me whakaoti te whārite x=\frac{5±13}{2} ina he tāpiri te ±. Tāpiri 5 ki te 13.

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

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{5±13}{2} ina he tango te ±. Tango 13 mai i 5.

$$x=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=9 x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$36=x^{2}-5x$$

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

$$x^{2}-5x=36$$

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.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=36+\left(-\frac{5}{2}\right)^{2}$$

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

$$x^{2}-5x+\frac{25}{4}=36+\frac{25}{4}$$

Tāpiri 36 ki te \frac{25}{4}.

$$x^{2}-5x+\frac{25}{4}=\frac{169}{4}$$

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}.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{169}{4}$$

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

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{169}{4}}$$

Whakarūnātia.

$$x-\frac{5}{2}=\frac{13}{2} x-\frac{5}{2}=-\frac{13}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$x=9 x=-4$$