Whakaoti i te 28=x(x+10)div2

$$28=x(x+10) \div 2$$

Whakaoti mō x

$$x=-14$$

$$x=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 2.

$$28\times 2=x\left(x+10\right)$$

Whakareatia te 28 ki te 2, ka 56.

$$56=x\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+10.

$$56=x^{2}+10x$$

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

$$x^{2}+10x=56$$

Tangohia te 56 mai i ngā taha e rua.

$$x^{2}+10x-56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 10 mō b, me -56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-56\right)}}{2}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\left(-56\right)}}{2}$$

Whakareatia -4 ki te -56.

$$x=\frac{-10±\sqrt{100+224}}{2}$$

Tāpiri 100 ki te 224.

$$x=\frac{-10±\sqrt{324}}{2}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-10±18}{2}$$

Nā, me whakaoti te whārite x=\frac{-10±18}{2} ina he tāpiri te ±. Tāpiri -10 ki te 18.

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

Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-10±18}{2} ina he tango te ±. Tango 18 mai i -10.

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

Whakawehe -28 ki te 2.

$$x=-14$$

Kua oti te whārite te whakatau.

$$x=4 x=-14$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua ki te 2.

$$28\times 2=x\left(x+10\right)$$

Whakareatia te 28 ki te 2, ka 56.

$$56=x\left(x+10\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+10.

$$56=x^{2}+10x$$

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

$$x^{2}+10x=56$$

Whakawehea te 10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 5. Nā, tāpiria te pūrua o te 5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+10x+5^{2}=56+5^{2}$$

Pūrua 5.

$$x^{2}+10x+25=56+25$$

Tāpiri 56 ki te 25.

$$x^{2}+10x+25=81$$

Tauwehea x^{2}+10x+25. 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}.

$$\left(x+5\right)^{2}=81$$

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

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{81}$$

Whakarūnātia.

$$x+5=9 x+5=-9$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$x=4 x=-14$$