Whakaoti i te 4left(x-3right)left(5x-19right)=4

$$4 \left( x-3 \right) \left( 5x-19 \right) = 4$$

Whakaoti mō x

$$x=4$$

$$x = \frac{14}{5} = 2\frac{4}{5} = 2.8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-3.

$$\left(4x-12\right)\left(5x-19\right)=4$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x-12 ki te 5x-19 ka whakakotahi i ngā kupu rite.

$$20x^{2}-136x+228=4$$

Tangohia te 4 mai i ngā taha e rua.

$$20x^{2}-136x+228-4=0$$

Tangohia te 4 i te 228, ka 224.

$$20x^{2}-136x+224=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 20 mō a, -136 mō b, me 224 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-136\right)±\sqrt{\left(-136\right)^{2}-4\times 20\times 224}}{2\times 20}$$

Pūrua -136.

$$x=\frac{-\left(-136\right)±\sqrt{18496-4\times 20\times 224}}{2\times 20}$$

Whakareatia -4 ki te 20.

$$x=\frac{-\left(-136\right)±\sqrt{18496-80\times 224}}{2\times 20}$$

Whakareatia -80 ki te 224.

$$x=\frac{-\left(-136\right)±\sqrt{18496-17920}}{2\times 20}$$

Tāpiri 18496 ki te -17920.

$$x=\frac{-\left(-136\right)±\sqrt{576}}{2\times 20}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-136\right)±24}{2\times 20}$$

Ko te tauaro o -136 ko 136.

$$x=\frac{136±24}{2\times 20}$$

Whakareatia 2 ki te 20.

$$x=\frac{136±24}{40}$$

Nā, me whakaoti te whārite x=\frac{136±24}{40} ina he tāpiri te ±. Tāpiri 136 ki te 24.

$$x=\frac{160}{40}$$

Whakawehe 160 ki te 40.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{136±24}{40} ina he tango te ±. Tango 24 mai i 136.

$$x=\frac{112}{40}$$

Whakahekea te hautanga \frac{112}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=\frac{14}{5}$$

Kua oti te whārite te whakatau.

$$x=4 x=\frac{14}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x-3.

$$\left(4x-12\right)\left(5x-19\right)=4$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4x-12 ki te 5x-19 ka whakakotahi i ngā kupu rite.

$$20x^{2}-136x+228=4$$

Tangohia te 228 mai i ngā taha e rua.

$$20x^{2}-136x=4-228$$

Tangohia te 228 i te 4, ka -224.

$$20x^{2}-136x=-224$$

Whakawehea ngā taha e rua ki te 20.

$$\frac{20x^{2}-136x}{20}=-\frac{224}{20}$$

Mā te whakawehe ki te 20 ka wetekia te whakareanga ki te 20.

$$x^{2}+\left(-\frac{136}{20}\right)x=-\frac{224}{20}$$

Whakahekea te hautanga \frac{-136}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{34}{5}x=-\frac{224}{20}$$

Whakahekea te hautanga \frac{-224}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{34}{5}x=-\frac{56}{5}$$

Whakawehea te -\frac{34}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{5}. Nā, tāpiria te pūrua o te -\frac{17}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{34}{5}x+\left(-\frac{17}{5}\right)^{2}=-\frac{56}{5}+\left(-\frac{17}{5}\right)^{2}$$

Pūruatia -\frac{17}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{34}{5}x+\frac{289}{25}=-\frac{56}{5}+\frac{289}{25}$$

Tāpiri -\frac{56}{5} ki te \frac{289}{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.

$$x^{2}-\frac{34}{5}x+\frac{289}{25}=\frac{9}{25}$$

Tauwehea x^{2}-\frac{34}{5}x+\frac{289}{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}.

$$\left(x-\frac{17}{5}\right)^{2}=\frac{9}{25}$$

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

$$\sqrt{\left(x-\frac{17}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Whakarūnātia.

$$x-\frac{17}{5}=\frac{3}{5} x-\frac{17}{5}=-\frac{3}{5}$$

Me tāpiri \frac{17}{5} ki ngā taha e rua o te whārite.

$$x=4 x=\frac{14}{5}$$