Whakaoti i te 40+0.085x^2=5x

$$40 + 0.085 x ^ { 2 } = 5 x$$

Whakaoti mō x

$$x = \frac{20 \sqrt{285} + 500}{17} \approx 49.272874137$$

$$x = \frac{500 - 20 \sqrt{285}}{17} \approx 9.550655275$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 5x mai i ngā taha e rua.

$$40+0.085x^{2}-5x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$0.085x^{2}-5x+40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.085 mō a, -5 mō b, me 40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 0.085\times 40}}{2\times 0.085}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 0.085\times 40}}{2\times 0.085}$$

Whakareatia -4 ki te 0.085.

$$x=\frac{-\left(-5\right)±\sqrt{25-0.34\times 40}}{2\times 0.085}$$

Whakareatia -0.34 ki te 40.

$$x=\frac{-\left(-5\right)±\sqrt{25-13.6}}{2\times 0.085}$$

Tāpiri 25 ki te -13.6.

$$x=\frac{-\left(-5\right)±\sqrt{11.4}}{2\times 0.085}$$

Tuhia te pūtakerua o te 11.4.

$$x=\frac{-\left(-5\right)±\frac{\sqrt{285}}{5}}{2\times 0.085}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\frac{\sqrt{285}}{5}}{2\times 0.085}$$

Whakareatia 2 ki te 0.085.

$$x=\frac{5±\frac{\sqrt{285}}{5}}{0.17}$$

Nā, me whakaoti te whārite x=\frac{5±\frac{\sqrt{285}}{5}}{0.17} ina he tāpiri te ±. Tāpiri 5 ki te \frac{\sqrt{285}}{5}.

$$x=\frac{\frac{\sqrt{285}}{5}+5}{0.17}$$

Whakawehe 5+\frac{\sqrt{285}}{5} ki te 0.17 mā te whakarea 5+\frac{\sqrt{285}}{5} ki te tau huripoki o 0.17.

$$x=\frac{20\sqrt{285}+500}{17}$$

Nā, me whakaoti te whārite x=\frac{5±\frac{\sqrt{285}}{5}}{0.17} ina he tango te ±. Tango \frac{\sqrt{285}}{5} mai i 5.

$$x=\frac{-\frac{\sqrt{285}}{5}+5}{0.17}$$

Whakawehe 5-\frac{\sqrt{285}}{5} ki te 0.17 mā te whakarea 5-\frac{\sqrt{285}}{5} ki te tau huripoki o 0.17.

$$x=\frac{500-20\sqrt{285}}{17}$$

Kua oti te whārite te whakatau.

$$x=\frac{20\sqrt{285}+500}{17} x=\frac{500-20\sqrt{285}}{17}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 5x mai i ngā taha e rua.

$$40+0.085x^{2}-5x=0$$

Tangohia te 40 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$0.085x^{2}-5x=-40$$

Whakawehea ngā taha e rua o te whārite ki te 0.085, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{0.085x^{2}-5x}{0.085}=-\frac{40}{0.085}$$

Mā te whakawehe ki te 0.085 ka wetekia te whakareanga ki te 0.085.

$$x^{2}+\left(-\frac{5}{0.085}\right)x=-\frac{40}{0.085}$$

Whakawehe -5 ki te 0.085 mā te whakarea -5 ki te tau huripoki o 0.085.

$$x^{2}-\frac{1000}{17}x=-\frac{40}{0.085}$$

Whakawehe -40 ki te 0.085 mā te whakarea -40 ki te tau huripoki o 0.085.

$$x^{2}-\frac{1000}{17}x=-\frac{8000}{17}$$

Whakawehea te -\frac{1000}{17}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{500}{17}. Nā, tāpiria te pūrua o te -\frac{500}{17} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1000}{17}x+\left(-\frac{500}{17}\right)^{2}=-\frac{8000}{17}+\left(-\frac{500}{17}\right)^{2}$$

Pūruatia -\frac{500}{17} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1000}{17}x+\frac{250000}{289}=-\frac{8000}{17}+\frac{250000}{289}$$

Tāpiri -\frac{8000}{17} ki te \frac{250000}{289} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{1000}{17}x+\frac{250000}{289}=\frac{114000}{289}$$

Tauwehea x^{2}-\frac{1000}{17}x+\frac{250000}{289}. 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}.

$$\left(x-\frac{500}{17}\right)^{2}=\frac{114000}{289}$$

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

$$\sqrt{\left(x-\frac{500}{17}\right)^{2}}=\sqrt{\frac{114000}{289}}$$

Whakarūnātia.

$$x-\frac{500}{17}=\frac{20\sqrt{285}}{17} x-\frac{500}{17}=-\frac{20\sqrt{285}}{17}$$

Me tāpiri \frac{500}{17} ki ngā taha e rua o te whārite.

$$x=\frac{20\sqrt{285}+500}{17} x=\frac{500-20\sqrt{285}}{17}$$