Whakaoti i te 0=4-0*x-0.5*9.8066*x^2

$$0=4-0 \times x-0.5 \times 9.8066 \times { x }^{ 2 }$$

Whakaoti mō x

$$x=\frac{200\sqrt{49033}}{49033}\approx 0.903203814$$

$$x=-\frac{200\sqrt{49033}}{49033}\approx -0.903203814$$

Ngā Upane mā te Kimi Pūtakerua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0=4-0-0.5\times 9.8066x^{2}$$

Tangohia te 0 i te 4, ka 4.

$$0=4-0.5\times 9.8066x^{2}$$

Whakareatia te 0.5 ki te 9.8066, ka 4.9033.

$$0=4-4.9033x^{2}$$

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

$$4-4.9033x^{2}=0$$

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-4.9033x^{2}=-4$$

Whakawehea ngā taha e rua ki te -4.9033.

$$x^{2}=\frac{-4}{-4.9033}$$

Whakarohaina te \frac{-4}{-4.9033} mā te whakarea i te taurunga me te tauraro ki te 10000.

$$x^{2}=\frac{-40000}{-49033}$$

Ka taea te hautanga \frac{-40000}{-49033} te whakamāmā ki te \frac{40000}{49033} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=\frac{40000}{49033}$$

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

$$x=\frac{200\sqrt{49033}}{49033} x=-\frac{200\sqrt{49033}}{49033}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0=4-0-0.5\times 9.8066x^{2}$$

Tangohia te 0 i te 4, ka 4.

$$0=4-0.5\times 9.8066x^{2}$$

Whakareatia te 0.5 ki te 9.8066, ka 4.9033.

$$0=4-4.9033x^{2}$$

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

$$4-4.9033x^{2}=0$$

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.

$$-4.9033x^{2}+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4.9033 mō a, 0 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4.9033\right)\times 4}}{2\left(-4.9033\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-4.9033\right)\times 4}}{2\left(-4.9033\right)}$$

Whakareatia -4 ki te -4.9033.

$$x=\frac{0±\sqrt{19.6132\times 4}}{2\left(-4.9033\right)}$$

Whakareatia 19.6132 ki te 4.

$$x=\frac{0±\sqrt{78.4528}}{2\left(-4.9033\right)}$$

Tuhia te pūtakerua o te 78.4528.

$$x=\frac{0±\frac{\sqrt{49033}}{25}}{2\left(-4.9033\right)}$$

Whakareatia 2 ki te -4.9033.

$$x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066} ina he tāpiri te ±.

$$x=-\frac{200\sqrt{49033}}{49033}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{\sqrt{49033}}{25}}{-9.8066} ina he tango te ±.

$$x=\frac{200\sqrt{49033}}{49033}$$

Kua oti te whārite te whakatau.

$$x=-\frac{200\sqrt{49033}}{49033} x=\frac{200\sqrt{49033}}{49033}$$