Whakaoti i te (6x-5)(3x-1)=(2x+1)(5x-3)

$$( 6 x - 5 ) ( 3 x - 1 ) = ( 2 x + 1 ) ( 5 x - 3 )$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-5 ki te 3x-1 ka whakakotahi i ngā kupu rite.

$$18x^{2}-21x+5=\left(2x+1\right)\left(5x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+1 ki te 5x-3 ka whakakotahi i ngā kupu rite.

$$18x^{2}-21x+5=10x^{2}-x-3$$

Tangohia te 10x^{2} mai i ngā taha e rua.

$$18x^{2}-21x+5-10x^{2}=-x-3$$

Pahekotia te 18x^{2} me -10x^{2}, ka 8x^{2}.

$$8x^{2}-21x+5=-x-3$$

Me tāpiri te x ki ngā taha e rua.

$$8x^{2}-21x+5+x=-3$$

Pahekotia te -21x me x, ka -20x.

$$8x^{2}-20x+5=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$8x^{2}-20x+5+3=0$$

Tāpirihia te 5 ki te 3, ka 8.

$$8x^{2}-20x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -20 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 8\times 8}}{2\times 8}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 8\times 8}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-\left(-20\right)±\sqrt{400-32\times 8}}{2\times 8}$$

Whakareatia -32 ki te 8.

$$x=\frac{-\left(-20\right)±\sqrt{400-256}}{2\times 8}$$

Tāpiri 400 ki te -256.

$$x=\frac{-\left(-20\right)±\sqrt{144}}{2\times 8}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-\left(-20\right)±12}{2\times 8}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±12}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{20±12}{16}$$

Nā, me whakaoti te whārite x=\frac{20±12}{16} ina he tāpiri te ±. Tāpiri 20 ki te 12.

$$x=\frac{32}{16}$$

Whakawehe 32 ki te 16.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{20±12}{16} ina he tango te ±. Tango 12 mai i 20.

$$x=\frac{8}{16}$$

Whakahekea te hautanga \frac{8}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x-5 ki te 3x-1 ka whakakotahi i ngā kupu rite.

$$18x^{2}-21x+5=\left(2x+1\right)\left(5x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+1 ki te 5x-3 ka whakakotahi i ngā kupu rite.

$$18x^{2}-21x+5=10x^{2}-x-3$$

Tangohia te 10x^{2} mai i ngā taha e rua.

$$18x^{2}-21x+5-10x^{2}=-x-3$$

Pahekotia te 18x^{2} me -10x^{2}, ka 8x^{2}.

$$8x^{2}-21x+5=-x-3$$

Me tāpiri te x ki ngā taha e rua.

$$8x^{2}-21x+5+x=-3$$

Pahekotia te -21x me x, ka -20x.

$$8x^{2}-20x+5=-3$$

Tangohia te 5 mai i ngā taha e rua.

$$8x^{2}-20x=-3-5$$

Tangohia te 5 i te -3, ka -8.

$$8x^{2}-20x=-8$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-20x}{8}=-\frac{8}{8}$$

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

$$x^{2}+\left(-\frac{20}{8}\right)x=-\frac{8}{8}$$

Whakahekea te hautanga \frac{-20}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{5}{2}x=-\frac{8}{8}$$

Whakawehe -8 ki te 8.

$$x^{2}-\frac{5}{2}x=-1$$

Whakawehea te -\frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{4}. Nā, tāpiria te pūrua o te -\frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=-1+\left(-\frac{5}{4}\right)^{2}$$

Pūruatia -\frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=-1+\frac{25}{16}$$

Tāpiri -1 ki te \frac{25}{16}.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{9}{16}$$

Tauwehea x^{2}-\frac{5}{2}x+\frac{25}{16}. 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}.

$$\left(x-\frac{5}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(x-\frac{5}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$x-\frac{5}{4}=\frac{3}{4} x-\frac{5}{4}=-\frac{3}{4}$$

Me tāpiri \frac{5}{4} ki ngā taha e rua o te whārite.

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