Whakaoti i te 5x(x+3)=3(x+3)

$$5 x ( x + 3 ) = 3 ( x + 3 )$$

Whakaoti mō x

$$x=-3$$

$$x=\frac{3}{5}=0.6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 5x ki te x+3.

$$5x^{2}+15x=3\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+3.

$$5x^{2}+15x=3x+9$$

Tangohia te 3x mai i ngā taha e rua.

$$5x^{2}+15x-3x=9$$

Pahekotia te 15x me -3x, ka 12x.

$$5x^{2}+12x=9$$

Tangohia te 9 mai i ngā taha e rua.

$$5x^{2}+12x-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 12 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 5\left(-9\right)}}{2\times 5}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 5\left(-9\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-12±\sqrt{144-20\left(-9\right)}}{2\times 5}$$

Whakareatia -20 ki te -9.

$$x=\frac{-12±\sqrt{144+180}}{2\times 5}$$

Tāpiri 144 ki te 180.

$$x=\frac{-12±\sqrt{324}}{2\times 5}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-12±18}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-12±18}{10}$$

Nā, me whakaoti te whārite x=\frac{-12±18}{10} ina he tāpiri te ±. Tāpiri -12 ki te 18.

$$x=\frac{6}{10}$$

Whakahekea te hautanga \frac{6}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{5}$$

Nā, me whakaoti te whārite x=\frac{-12±18}{10} ina he tango te ±. Tango 18 mai i -12.

$$x=-\frac{30}{10}$$

Whakawehe -30 ki te 10.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{5} x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 5x ki te x+3.

$$5x^{2}+15x=3\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x+3.

$$5x^{2}+15x=3x+9$$

Tangohia te 3x mai i ngā taha e rua.

$$5x^{2}+15x-3x=9$$

Pahekotia te 15x me -3x, ka 12x.

$$5x^{2}+12x=9$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}+12x}{5}=\frac{9}{5}$$

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

$$x^{2}+\frac{12}{5}x=\frac{9}{5}$$

Whakawehea te \frac{12}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{6}{5}. Nā, tāpiria te pūrua o te \frac{6}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{12}{5}x+\left(\frac{6}{5}\right)^{2}=\frac{9}{5}+\left(\frac{6}{5}\right)^{2}$$

Pūruatia \frac{6}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{12}{5}x+\frac{36}{25}=\frac{9}{5}+\frac{36}{25}$$

Tāpiri \frac{9}{5} ki te \frac{36}{25} 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.

$$x^{2}+\frac{12}{5}x+\frac{36}{25}=\frac{81}{25}$$

Tauwehea x^{2}+\frac{12}{5}x+\frac{36}{25}. 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}.

$$\left(x+\frac{6}{5}\right)^{2}=\frac{81}{25}$$

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

$$\sqrt{\left(x+\frac{6}{5}\right)^{2}}=\sqrt{\frac{81}{25}}$$

Whakarūnātia.

$$x+\frac{6}{5}=\frac{9}{5} x+\frac{6}{5}=-\frac{9}{5}$$

Me tango \frac{6}{5} mai i ngā taha e rua o te whārite.

$$x=\frac{3}{5} x=-3$$