Whakaoti i te 1/2*30*(25.3^2-x^2)=-30*15.5

$$\frac{ 1 }{ 2 } \times 30 \times ( { 25.3 }^{ 2 } - { x }^{ 2 } )=-30 \times 15.5$$

Whakaoti mō x

$$x = \frac{\sqrt{67109}}{10} \approx 25.905404841$$

$$x = -\frac{\sqrt{67109}}{10} \approx -25.905404841$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te \frac{1}{2} ki te 30, ka 15.

$$15\left(25.3^{2}-x^{2}\right)=-30\times 15.5$$

Tātaihia te 25.3 mā te pū o 2, kia riro ko 640.09.

$$15\left(640.09-x^{2}\right)=-30\times 15.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 15 ki te 640.09-x^{2}.

$$9601.35-15x^{2}=-30\times 15.5$$

Whakareatia te -30 ki te 15.5, ka -465.

$$9601.35-15x^{2}=-465$$

Tangohia te 9601.35 mai i ngā taha e rua.

$$-15x^{2}=-465-9601.35$$

Tangohia te 9601.35 i te -465, ka -10066.35.

$$-15x^{2}=-10066.35$$

Whakawehea ngā taha e rua ki te -15.

$$x^{2}=\frac{-10066.35}{-15}$$

Whakarohaina te \frac{-10066.35}{-15} mā te whakarea i te taurunga me te tauraro ki te 100.

$$x^{2}=\frac{-1006635}{-1500}$$

Whakahekea te hautanga \frac{-1006635}{-1500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -15.

$$x^{2}=\frac{67109}{100}$$

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

$$x=\frac{\sqrt{67109}}{10} x=-\frac{\sqrt{67109}}{10}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 30, ka 15.

$$15\left(25.3^{2}-x^{2}\right)=-30\times 15.5$$

Tātaihia te 25.3 mā te pū o 2, kia riro ko 640.09.

$$15\left(640.09-x^{2}\right)=-30\times 15.5$$

Whakamahia te āhuatanga tohatoha hei whakarea te 15 ki te 640.09-x^{2}.

$$9601.35-15x^{2}=-30\times 15.5$$

Whakareatia te -30 ki te 15.5, ka -465.

$$9601.35-15x^{2}=-465$$

Me tāpiri te 465 ki ngā taha e rua.

$$9601.35-15x^{2}+465=0$$

Tāpirihia te 9601.35 ki te 465, ka 10066.35.

$$10066.35-15x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-15x^{2}+10066.35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -15 mō a, 0 mō b, me 10066.35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 10066.35}}{2\left(-15\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 10066.35}}{2\left(-15\right)}$$

Whakareatia -4 ki te -15.

$$x=\frac{0±\sqrt{60\times 10066.35}}{2\left(-15\right)}$$

Whakareatia 60 ki te 10066.35.

$$x=\frac{0±\sqrt{603981}}{2\left(-15\right)}$$

Tuhia te pūtakerua o te 603981.

$$x=\frac{0±3\sqrt{67109}}{2\left(-15\right)}$$

Whakareatia 2 ki te -15.

$$x=\frac{0±3\sqrt{67109}}{-30}$$

Nā, me whakaoti te whārite x=\frac{0±3\sqrt{67109}}{-30} ina he tāpiri te ±.

$$x=-\frac{\sqrt{67109}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±3\sqrt{67109}}{-30} ina he tango te ±.

$$x=\frac{\sqrt{67109}}{10}$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{67109}}{10} x=\frac{\sqrt{67109}}{10}$$