Whakaoti i te 5x^2+17x=12x

$$5 x ^ { 2 } + 17 x = 12 x$$

Whakaoti mō x

$$x=-1$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 12x mai i ngā taha e rua.

$$5x^{2}+17x-12x=0$$

Pahekotia te 17x me -12x, ka 5x.

$$5x^{2}+5x=0$$

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

$$x=\frac{-5±\sqrt{5^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te 5^{2}.

$$x=\frac{-5±5}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-5±5}{10}$$

Nā, me whakaoti te whārite x=\frac{-5±5}{10} ina he tāpiri te ±. Tāpiri -5 ki te 5.

$$x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-5±5}{10} ina he tango te ±. Tango 5 mai i -5.

$$x=-\frac{10}{10}$$

Whakawehe -10 ki te 10.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=0 x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 12x mai i ngā taha e rua.

$$5x^{2}+17x-12x=0$$

Pahekotia te 17x me -12x, ka 5x.

$$5x^{2}+5x=0$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}+5x}{5}=\frac{0}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}+\frac{5}{5}x=\frac{0}{5}$$

Whakawehe 5 ki te 5.

$$x^{2}+x=\frac{0}{5}$$

Whakawehe 0 ki te 5.

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

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=\frac{1}{4}$$

Tauwehea x^{2}+x+\frac{1}{4}. 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}.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{1}{2} x+\frac{1}{2}=-\frac{1}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-1$$