Whakaoti i te x^2+16x/13+40x/9=0

$$x ^ { 2 } + \frac { 16 x } { 13 } + \frac { 40 x } { 9 } = 0$$

Whakaoti mō x

$$x = -\frac{664}{117} = -5\frac{79}{117} \approx -5.675213675$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me whakarea ngā taha e rua o te whārite ki te 117, arā, te tauraro pātahi he tino iti rawa te kitea o 13,9.

$$117x^{2}+9\times 16x+13\times 40x=0$$

Whakareatia te 9 ki te 16, ka 144.

$$117x^{2}+144x+13\times 40x=0$$

Whakareatia te 13 ki te 40, ka 520.

$$117x^{2}+144x+520x=0$$

Pahekotia te 144x me 520x, ka 664x.

$$117x^{2}+664x=0$$

Tauwehea te x.

$$x\left(117x+664\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 117x+664=0.

$$x=0 x=-\frac{664}{117}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 117, arā, te tauraro pātahi he tino iti rawa te kitea o 13,9.

$$117x^{2}+9\times 16x+13\times 40x=0$$

Whakareatia te 9 ki te 16, ka 144.

$$117x^{2}+144x+13\times 40x=0$$

Whakareatia te 13 ki te 40, ka 520.

$$117x^{2}+144x+520x=0$$

Pahekotia te 144x me 520x, ka 664x.

$$117x^{2}+664x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 117 mō a, 664 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-664±\sqrt{664^{2}}}{2\times 117}$$

Tuhia te pūtakerua o te 664^{2}.

$$x=\frac{-664±664}{2\times 117}$$

Whakareatia 2 ki te 117.

$$x=\frac{-664±664}{234}$$

Nā, me whakaoti te whārite x=\frac{-664±664}{234} ina he tāpiri te ±. Tāpiri -664 ki te 664.

$$x=\frac{0}{234}$$

Whakawehe 0 ki te 234.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-664±664}{234} ina he tango te ±. Tango 664 mai i -664.

$$x=-\frac{1328}{234}$$

Whakahekea te hautanga \frac{-1328}{234} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{664}{117}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{664}{117}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 117, arā, te tauraro pātahi he tino iti rawa te kitea o 13,9.

$$117x^{2}+9\times 16x+13\times 40x=0$$

Whakareatia te 9 ki te 16, ka 144.

$$117x^{2}+144x+13\times 40x=0$$

Whakareatia te 13 ki te 40, ka 520.

$$117x^{2}+144x+520x=0$$

Pahekotia te 144x me 520x, ka 664x.

$$117x^{2}+664x=0$$

Whakawehea ngā taha e rua ki te 117.

$$\frac{117x^{2}+664x}{117}=\frac{0}{117}$$

Mā te whakawehe ki te 117 ka wetekia te whakareanga ki te 117.

$$x^{2}+\frac{664}{117}x=\frac{0}{117}$$

Whakawehe 0 ki te 117.

$$x^{2}+\frac{664}{117}x=0$$

Whakawehea te \frac{664}{117}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{332}{117}. Nā, tāpiria te pūrua o te \frac{332}{117} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{664}{117}x+\left(\frac{332}{117}\right)^{2}=\left(\frac{332}{117}\right)^{2}$$

Pūruatia \frac{332}{117} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{664}{117}x+\frac{110224}{13689}=\frac{110224}{13689}$$

Tauwehea x^{2}+\frac{664}{117}x+\frac{110224}{13689}. 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}.

$$\left(x+\frac{332}{117}\right)^{2}=\frac{110224}{13689}$$

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

$$\sqrt{\left(x+\frac{332}{117}\right)^{2}}=\sqrt{\frac{110224}{13689}}$$

Whakarūnātia.

$$x+\frac{332}{117}=\frac{332}{117} x+\frac{332}{117}=-\frac{332}{117}$$

Me tango \frac{332}{117} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{664}{117}$$