Whakaoti i te 2x(5x-3)=2(4x+3)

$$2x(5x-3)=2(4x+3)$$

Whakaoti mō x

$$x = \frac{\sqrt{109} + 7}{10} \approx 1.744030651$$

$$x=\frac{7-\sqrt{109}}{10}\approx -0.344030651$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakakore te 2 ki ngā taha e rua.

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

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

$$5x^{2}-3x=4x+3$$

Tangohia te 4x mai i ngā taha e rua.

$$5x^{2}-3x-4x=3$$

Pahekotia te -3x me -4x, ka -7x.

$$5x^{2}-7x=3$$

Tangohia te 3 mai i ngā taha e rua.

$$5x^{2}-7x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -7 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 5\left(-3\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-7\right)±\sqrt{49-20\left(-3\right)}}{2\times 5}$$

Whakareatia -20 ki te -3.

$$x=\frac{-\left(-7\right)±\sqrt{49+60}}{2\times 5}$$

Tāpiri 49 ki te 60.

$$x=\frac{-\left(-7\right)±\sqrt{109}}{2\times 5}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±\sqrt{109}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{7±\sqrt{109}}{10}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{109}}{10} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{109}.

$$x=\frac{\sqrt{109}+7}{10}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{109}}{10} ina he tango te ±. Tango \sqrt{109} mai i 7.

$$x=\frac{7-\sqrt{109}}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{109}+7}{10} x=\frac{7-\sqrt{109}}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakakore te 2 ki ngā taha e rua.

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

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

$$5x^{2}-3x=4x+3$$

Tangohia te 4x mai i ngā taha e rua.

$$5x^{2}-3x-4x=3$$

Pahekotia te -3x me -4x, ka -7x.

$$5x^{2}-7x=3$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-7x}{5}=\frac{3}{5}$$

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

$$x^{2}-\frac{7}{5}x=\frac{3}{5}$$

Whakawehea te -\frac{7}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{10}. Nā, tāpiria te pūrua o te -\frac{7}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7}{5}x+\left(-\frac{7}{10}\right)^{2}=\frac{3}{5}+\left(-\frac{7}{10}\right)^{2}$$

Pūruatia -\frac{7}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{5}x+\frac{49}{100}=\frac{3}{5}+\frac{49}{100}$$

Tāpiri \frac{3}{5} ki te \frac{49}{100} 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.

$$x^{2}-\frac{7}{5}x+\frac{49}{100}=\frac{109}{100}$$

Tauwehea x^{2}-\frac{7}{5}x+\frac{49}{100}. 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}.

$$\left(x-\frac{7}{10}\right)^{2}=\frac{109}{100}$$

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

$$\sqrt{\left(x-\frac{7}{10}\right)^{2}}=\sqrt{\frac{109}{100}}$$

Whakarūnātia.

$$x-\frac{7}{10}=\frac{\sqrt{109}}{10} x-\frac{7}{10}=-\frac{\sqrt{109}}{10}$$

Me tāpiri \frac{7}{10} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{109}+7}{10} x=\frac{7-\sqrt{109}}{10}$$