Whakaoti i te -49w^2+9=0

$$- 49 w ^ { 2 } + 9 = 0$$

Whakaoti mō w

$$w=\frac{3}{7}\approx 0.428571429$$

$$w=-\frac{3}{7}\approx -0.428571429$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 9 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-49w^{2}=-9$$

Whakawehea ngā taha e rua ki te -49.

$$w^{2}=\frac{-9}{-49}$$

Ka taea te hautanga \frac{-9}{-49} te whakamāmā ki te \frac{9}{49} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$w^{2}=\frac{9}{49}$$

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

$$w=\frac{3}{7} w=-\frac{3}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-49w^{2}+9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -49 mō a, 0 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\left(-49\right)\times 9}}{2\left(-49\right)}$$

Pūrua 0.

$$w=\frac{0±\sqrt{-4\left(-49\right)\times 9}}{2\left(-49\right)}$$

Whakareatia -4 ki te -49.

$$w=\frac{0±\sqrt{196\times 9}}{2\left(-49\right)}$$

Whakareatia 196 ki te 9.

$$w=\frac{0±\sqrt{1764}}{2\left(-49\right)}$$

Tuhia te pūtakerua o te 1764.

$$w=\frac{0±42}{2\left(-49\right)}$$

Whakareatia 2 ki te -49.

$$w=\frac{0±42}{-98}$$

Nā, me whakaoti te whārite w=\frac{0±42}{-98} ina he tāpiri te ±. Whakahekea te hautanga \frac{42}{-98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$w=-\frac{3}{7}$$

Nā, me whakaoti te whārite w=\frac{0±42}{-98} ina he tango te ±. Whakahekea te hautanga \frac{-42}{-98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$w=\frac{3}{7}$$

Kua oti te whārite te whakatau.

$$w=-\frac{3}{7} w=\frac{3}{7}$$