Whakaoti i te 1/2*30*(253^2-x^2)=-30*155

$$\frac{ 1 }{ 2 } \times 30 \times ( { 253 }^{ 2 } - { x }^{ 2 } )=-30 \times 155$$

Whakaoti mō x

$$x=\sqrt{64319}\approx 253.611908238$$

$$x=-\sqrt{64319}\approx -253.611908238$$

Ngā Upane mā te Kimi Pūtakerua

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

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

Tātaihia te 253 mā te pū o 2, kia riro ko 64009.

$$15\left(64009-x^{2}\right)=-30\times 155$$

Whakamahia te āhuatanga tohatoha hei whakarea te 15 ki te 64009-x^{2}.

$$960135-15x^{2}=-30\times 155$$

Whakareatia te -30 ki te 155, ka -4650.

$$960135-15x^{2}=-4650$$

Tangohia te 960135 mai i ngā taha e rua.

$$-15x^{2}=-4650-960135$$

Tangohia te 960135 i te -4650, ka -964785.

$$-15x^{2}=-964785$$

Whakawehea ngā taha e rua ki te -15.

$$x^{2}=\frac{-964785}{-15}$$

Whakawehea te -964785 ki te -15, kia riro ko 64319.

$$x^{2}=64319$$

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

$$x=\sqrt{64319} x=-\sqrt{64319}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$15\left(253^{2}-x^{2}\right)=-30\times 155$$

Tātaihia te 253 mā te pū o 2, kia riro ko 64009.

$$15\left(64009-x^{2}\right)=-30\times 155$$

Whakamahia te āhuatanga tohatoha hei whakarea te 15 ki te 64009-x^{2}.

$$960135-15x^{2}=-30\times 155$$

Whakareatia te -30 ki te 155, ka -4650.

$$960135-15x^{2}=-4650$$

Me tāpiri te 4650 ki ngā taha e rua.

$$960135-15x^{2}+4650=0$$

Tāpirihia te 960135 ki te 4650, ka 964785.

$$964785-15x^{2}=0$$

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.

$$-15x^{2}+964785=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -15 mō a, 0 mō b, me 964785 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)\times 964785}}{2\left(-15\right)}$$

Whakareatia -4 ki te -15.

$$x=\frac{0±\sqrt{60\times 964785}}{2\left(-15\right)}$$

Whakareatia 60 ki te 964785.

$$x=\frac{0±\sqrt{57887100}}{2\left(-15\right)}$$

Tuhia te pūtakerua o te 57887100.

$$x=\frac{0±30\sqrt{64319}}{2\left(-15\right)}$$

Whakareatia 2 ki te -15.

$$x=\frac{0±30\sqrt{64319}}{-30}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{64319}}{-30} ina he tāpiri te ±.

$$x=-\sqrt{64319}$$

Nā, me whakaoti te whārite x=\frac{0±30\sqrt{64319}}{-30} ina he tango te ±.

$$x=\sqrt{64319}$$

Kua oti te whārite te whakatau.

$$x=-\sqrt{64319} x=\sqrt{64319}$$