Whakaoti i te 1/2[x+(x+14)](x-05)=405

$$\frac { 1 } { 2 } [ x + ( x + 14 ) ] ( x - 05 ) = 405$$

Whakaoti mō x

$$x = \frac{\sqrt{1669} - 7}{2} \approx 16.926698216$$

$$x=\frac{-\sqrt{1669}-7}{2}\approx -23.926698216$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x me x, ka 2x.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\times 5\right)=405$$

Whakareatia te 0 ki te 5, ka 0.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\right)=405$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 2x+14.

$$\left(x+7\right)\left(x-0\right)=405$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+7 ki te x-0.

$$x\left(x-0\right)+7\left(x-0\right)=405$$

Tangohia te 405 mai i ngā taha e rua.

$$x\left(x-0\right)+7\left(x-0\right)-405=0$$

Whakaraupapatia anō ngā kīanga tau.

$$xx+7x-405=0$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+7x-405=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me -405 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-405\right)}}{2}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-405\right)}}{2}$$

Whakareatia -4 ki te -405.

$$x=\frac{-7±\sqrt{49+1620}}{2}$$

Tāpiri 49 ki te 1620.

$$x=\frac{-7±\sqrt{1669}}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{1669}}{2} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{1669}.

$$x=\frac{\sqrt{1669}-7}{2}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{1669}}{2} ina he tango te ±. Tango \sqrt{1669} mai i -7.

$$x=\frac{-\sqrt{1669}-7}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{1669}-7}{2} x=\frac{-\sqrt{1669}-7}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te x me x, ka 2x.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\times 5\right)=405$$

Whakareatia te 0 ki te 5, ka 0.

$$\frac{1}{2}\left(2x+14\right)\left(x-0\right)=405$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 2x+14.

$$\left(x+7\right)\left(x-0\right)=405$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+7 ki te x-0.

$$x\left(x-0\right)+7\left(x-0\right)=405$$

Whakaraupapatia anō ngā kīanga tau.

$$xx+7x=405$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}+7x=405$$

Whakawehea te 7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{2}. Nā, tāpiria te pūrua o te \frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=405+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+7x+\frac{49}{4}=405+\frac{49}{4}$$

Tāpiri 405 ki te \frac{49}{4}.

$$x^{2}+7x+\frac{49}{4}=\frac{1669}{4}$$

Tauwehea x^{2}+7x+\frac{49}{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}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{1669}{4}$$

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

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{1669}{4}}$$

Whakarūnātia.

$$x+\frac{7}{2}=\frac{\sqrt{1669}}{2} x+\frac{7}{2}=-\frac{\sqrt{1669}}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{1669}-7}{2} x=\frac{-\sqrt{1669}-7}{2}$$