Whakaoti i te 15=x(x+16)

$$15=x(x+16)$$

Whakaoti mō x (complex solution)

$$x=\sqrt{79}-8\approx 0.888194417$$

$$x=-\left(\sqrt{79}+8\right)\approx -16.888194417$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$15=x^{2}+16x$$

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

$$x^{2}+16x=15$$

Tangohia te 15 mai i ngā taha e rua.

$$x^{2}+16x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-16±\sqrt{256+60}}{2}$$

Tāpiri 256 ki te 60.

$$x=\frac{-16±\sqrt{316}}{2}$$

Tuhia te pūtakerua o te 316.

$$x=\frac{-16±2\sqrt{79}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{79}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{79}.

$$x=\frac{2\sqrt{79}-16}{2}$$

Whakawehe -16+2\sqrt{79} ki te 2.

$$x=\sqrt{79}-8$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{79}}{2} ina he tango te ±. Tango 2\sqrt{79} mai i -16.

$$x=\frac{-2\sqrt{79}-16}{2}$$

Whakawehe -16-2\sqrt{79} ki te 2.

$$x=-\sqrt{79}-8$$

Kua oti te whārite te whakatau.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$15=x^{2}+16x$$

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

$$x^{2}+16x=15$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=15+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=15+64$$

Tāpiri 15 ki te 64.

$$x^{2}+16x+64=79$$

Tauwehea x^{2}+16x+64. 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}.

$$\left(x+8\right)^{2}=79$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{79}$$

Whakarūnātia.

$$x+8=\sqrt{79} x+8=-\sqrt{79}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Whakaoti mō x

$$x=\sqrt{79}-8\approx 0.888194417$$

$$x=-\sqrt{79}-8\approx -16.888194417$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$15=x^{2}+16x$$

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

$$x^{2}+16x=15$$

Tangohia te 15 mai i ngā taha e rua.

$$x^{2}+16x-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-15\right)}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$x=\frac{-16±\sqrt{256+60}}{2}$$

Tāpiri 256 ki te 60.

$$x=\frac{-16±\sqrt{316}}{2}$$

Tuhia te pūtakerua o te 316.

$$x=\frac{-16±2\sqrt{79}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{79}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{79}.

$$x=\frac{2\sqrt{79}-16}{2}$$

Whakawehe -16+2\sqrt{79} ki te 2.

$$x=\sqrt{79}-8$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{79}}{2} ina he tango te ±. Tango 2\sqrt{79} mai i -16.

$$x=\frac{-2\sqrt{79}-16}{2}$$

Whakawehe -16-2\sqrt{79} ki te 2.

$$x=-\sqrt{79}-8$$

Kua oti te whārite te whakatau.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+16.

$$15=x^{2}+16x$$

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

$$x^{2}+16x=15$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=15+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=15+64$$

Tāpiri 15 ki te 64.

$$x^{2}+16x+64=79$$

Tauwehea x^{2}+16x+64. 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}.

$$\left(x+8\right)^{2}=79$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{79}$$

Whakarūnātia.

$$x+8=\sqrt{79} x+8=-\sqrt{79}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$x=\sqrt{79}-8 x=-\sqrt{79}-8$$