Whakaoti i te (x-2)*180*x=144

$$(x-2) \times 180 \times x=144$$

Whakaoti mō x

$$x=\frac{3\sqrt{5}}{5}+1\approx 2.341640786$$

$$x=-\frac{3\sqrt{5}}{5}+1\approx -0.341640786$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 180.

$$\left(180x-360\right)x=144$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180x-360 ki te x.

$$180x^{2}-360x=144$$

Tangohia te 144 mai i ngā taha e rua.

$$180x^{2}-360x-144=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 180 mō a, -360 mō b, me -144 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-360\right)±\sqrt{\left(-360\right)^{2}-4\times 180\left(-144\right)}}{2\times 180}$$

Pūrua -360.

$$x=\frac{-\left(-360\right)±\sqrt{129600-4\times 180\left(-144\right)}}{2\times 180}$$

Whakareatia -4 ki te 180.

$$x=\frac{-\left(-360\right)±\sqrt{129600-720\left(-144\right)}}{2\times 180}$$

Whakareatia -720 ki te -144.

$$x=\frac{-\left(-360\right)±\sqrt{129600+103680}}{2\times 180}$$

Tāpiri 129600 ki te 103680.

$$x=\frac{-\left(-360\right)±\sqrt{233280}}{2\times 180}$$

Tuhia te pūtakerua o te 233280.

$$x=\frac{-\left(-360\right)±216\sqrt{5}}{2\times 180}$$

Ko te tauaro o -360 ko 360.

$$x=\frac{360±216\sqrt{5}}{2\times 180}$$

Whakareatia 2 ki te 180.

$$x=\frac{360±216\sqrt{5}}{360}$$

Nā, me whakaoti te whārite x=\frac{360±216\sqrt{5}}{360} ina he tāpiri te ±. Tāpiri 360 ki te 216\sqrt{5}.

$$x=\frac{216\sqrt{5}+360}{360}$$

Whakawehe 360+216\sqrt{5} ki te 360.

$$x=\frac{3\sqrt{5}}{5}+1$$

Nā, me whakaoti te whārite x=\frac{360±216\sqrt{5}}{360} ina he tango te ±. Tango 216\sqrt{5} mai i 360.

$$x=\frac{360-216\sqrt{5}}{360}$$

Whakawehe 360-216\sqrt{5} ki te 360.

$$x=-\frac{3\sqrt{5}}{5}+1$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{5}}{5}+1 x=-\frac{3\sqrt{5}}{5}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 180.

$$\left(180x-360\right)x=144$$

Whakamahia te āhuatanga tohatoha hei whakarea te 180x-360 ki te x.

$$180x^{2}-360x=144$$

Whakawehea ngā taha e rua ki te 180.

$$\frac{180x^{2}-360x}{180}=\frac{144}{180}$$

Mā te whakawehe ki te 180 ka wetekia te whakareanga ki te 180.

$$x^{2}+\left(-\frac{360}{180}\right)x=\frac{144}{180}$$

Whakawehe -360 ki te 180.

$$x^{2}-2x=\frac{144}{180}$$

Whakahekea te hautanga \frac{144}{180} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 36.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2x+1=\frac{4}{5}+1$$

Tāpiri \frac{4}{5} ki te 1.

$$x^{2}-2x+1=\frac{9}{5}$$

Tauwehea x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=\frac{9}{5}$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{9}{5}}$$

Whakarūnātia.

$$x-1=\frac{3\sqrt{5}}{5} x-1=-\frac{3\sqrt{5}}{5}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{5}}{5}+1 x=-\frac{3\sqrt{5}}{5}+1$$