Whakaoti i te 4x(x+5)=6x-4x^2

$$4 x ( x + 5 ) = 6 x - 4 x ^ { 2 }$$

Whakaoti mō x

$$x = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x+5.

$$4x^{2}+20x=6x-4x^{2}$$

Tangohia te 6x mai i ngā taha e rua.

$$4x^{2}+20x-6x=-4x^{2}$$

Pahekotia te 20x me -6x, ka 14x.

$$4x^{2}+14x=-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$4x^{2}+14x+4x^{2}=0$$

Pahekotia te 4x^{2} me 4x^{2}, ka 8x^{2}.

$$8x^{2}+14x=0$$

Tauwehea te x.

$$x\left(8x+14\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 8x+14=0.

$$x=0 x=-\frac{7}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x+5.

$$4x^{2}+20x=6x-4x^{2}$$

Tangohia te 6x mai i ngā taha e rua.

$$4x^{2}+20x-6x=-4x^{2}$$

Pahekotia te 20x me -6x, ka 14x.

$$4x^{2}+14x=-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$4x^{2}+14x+4x^{2}=0$$

Pahekotia te 4x^{2} me 4x^{2}, ka 8x^{2}.

$$8x^{2}+14x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 14 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}}}{2\times 8}$$

Tuhia te pūtakerua o te 14^{2}.

$$x=\frac{-14±14}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{-14±14}{16}$$

Nā, me whakaoti te whārite x=\frac{-14±14}{16} ina he tāpiri te ±. Tāpiri -14 ki te 14.

$$x=\frac{0}{16}$$

Whakawehe 0 ki te 16.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-14±14}{16} ina he tango te ±. Tango 14 mai i -14.

$$x=-\frac{28}{16}$$

Whakahekea te hautanga \frac{-28}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{7}{4}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{7}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x+5.

$$4x^{2}+20x=6x-4x^{2}$$

Tangohia te 6x mai i ngā taha e rua.

$$4x^{2}+20x-6x=-4x^{2}$$

Pahekotia te 20x me -6x, ka 14x.

$$4x^{2}+14x=-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$4x^{2}+14x+4x^{2}=0$$

Pahekotia te 4x^{2} me 4x^{2}, ka 8x^{2}.

$$8x^{2}+14x=0$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}+14x}{8}=\frac{0}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}+\frac{14}{8}x=\frac{0}{8}$$

Whakahekea te hautanga \frac{14}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{7}{4}x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x^{2}+\frac{7}{4}x=0$$

Whakawehea te \frac{7}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{8}. Nā, tāpiria te pūrua o te \frac{7}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{7}{4}x+\left(\frac{7}{8}\right)^{2}=\left(\frac{7}{8}\right)^{2}$$

Pūruatia \frac{7}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{7}{4}x+\frac{49}{64}=\frac{49}{64}$$

Tauwehea x^{2}+\frac{7}{4}x+\frac{49}{64}. 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}.

$$\left(x+\frac{7}{8}\right)^{2}=\frac{49}{64}$$

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

$$\sqrt{\left(x+\frac{7}{8}\right)^{2}}=\sqrt{\frac{49}{64}}$$

Whakarūnātia.

$$x+\frac{7}{8}=\frac{7}{8} x+\frac{7}{8}=-\frac{7}{8}$$

Me tango \frac{7}{8} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{7}{4}$$