Whakaoti i te 0=-16x^2+17x+7

$$0=-16 { x }^{ 2 } +17x+7$$

Whakaoti mō x

$$x = \frac{\sqrt{737} + 17}{32} \approx 1.379616998$$

$$x=\frac{17-\sqrt{737}}{32}\approx -0.317116998$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$-16x^{2}+17x+7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -16 mō a, 17 mō b, me 7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\left(-16\right)\times 7}}{2\left(-16\right)}$$

Pūrua 17.

$$x=\frac{-17±\sqrt{289-4\left(-16\right)\times 7}}{2\left(-16\right)}$$

Whakareatia -4 ki te -16.

$$x=\frac{-17±\sqrt{289+64\times 7}}{2\left(-16\right)}$$

Whakareatia 64 ki te 7.

$$x=\frac{-17±\sqrt{289+448}}{2\left(-16\right)}$$

Tāpiri 289 ki te 448.

$$x=\frac{-17±\sqrt{737}}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$x=\frac{-17±\sqrt{737}}{-32}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{737}}{-32} ina he tāpiri te ±. Tāpiri -17 ki te \sqrt{737}.

$$x=\frac{\sqrt{737}-17}{-32}$$

Whakawehe -17+\sqrt{737} ki te -32.

$$x=\frac{17-\sqrt{737}}{32}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{737}}{-32} ina he tango te ±. Tango \sqrt{737} mai i -17.

$$x=\frac{-\sqrt{737}-17}{-32}$$

Whakawehe -17-\sqrt{737} ki te -32.

$$x=\frac{\sqrt{737}+17}{32}$$

Kua oti te whārite te whakatau.

$$x=\frac{17-\sqrt{737}}{32} x=\frac{\sqrt{737}+17}{32}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$-16x^{2}+17x+7=0$$

Tangohia te 7 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-16x^{2}+17x=-7$$

Whakawehea ngā taha e rua ki te -16.

$$\frac{-16x^{2}+17x}{-16}=-\frac{7}{-16}$$

Mā te whakawehe ki te -16 ka wetekia te whakareanga ki te -16.

$$x^{2}+\frac{17}{-16}x=-\frac{7}{-16}$$

Whakawehe 17 ki te -16.

$$x^{2}-\frac{17}{16}x=-\frac{7}{-16}$$

Whakawehe -7 ki te -16.

$$x^{2}-\frac{17}{16}x=\frac{7}{16}$$

Whakawehea te -\frac{17}{16}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{32}. Nā, tāpiria te pūrua o te -\frac{17}{32} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{17}{16}x+\left(-\frac{17}{32}\right)^{2}=\frac{7}{16}+\left(-\frac{17}{32}\right)^{2}$$

Pūruatia -\frac{17}{32} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{17}{16}x+\frac{289}{1024}=\frac{7}{16}+\frac{289}{1024}$$

Tāpiri \frac{7}{16} ki te \frac{289}{1024} 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.

$$x^{2}-\frac{17}{16}x+\frac{289}{1024}=\frac{737}{1024}$$

Tauwehea x^{2}-\frac{17}{16}x+\frac{289}{1024}. 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}.

$$\left(x-\frac{17}{32}\right)^{2}=\frac{737}{1024}$$

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

$$\sqrt{\left(x-\frac{17}{32}\right)^{2}}=\sqrt{\frac{737}{1024}}$$

Whakarūnātia.

$$x-\frac{17}{32}=\frac{\sqrt{737}}{32} x-\frac{17}{32}=-\frac{\sqrt{737}}{32}$$

Me tāpiri \frac{17}{32} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{737}+17}{32} x=\frac{17-\sqrt{737}}{32}$$