Whakaoti i te (25-2x+1)x=80

$$(25-2x+1)x=80$$

Whakaoti mō x

$$x=5$$

$$x=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 25 ki te 1, ka 26.

$$\left(26-2x\right)x=80$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26-2x ki te x.

$$26x-2x^{2}=80$$

Tangohia te 80 mai i ngā taha e rua.

$$26x-2x^{2}-80=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-2x^{2}+26x-80=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 26 mō b, me -80 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

Pūrua 26.

$$x=\frac{-26±\sqrt{676-4\left(-2\right)\left(-80\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-26±\sqrt{676+8\left(-80\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -80.

$$x=\frac{-26±\sqrt{676-640}}{2\left(-2\right)}$$

Tāpiri 676 ki te -640.

$$x=\frac{-26±\sqrt{36}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-26±6}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-26±6}{-4}$$

Nā, me whakaoti te whārite x=\frac{-26±6}{-4} ina he tāpiri te ±. Tāpiri -26 ki te 6.

$$x=-\frac{20}{-4}$$

Whakawehe -20 ki te -4.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{-26±6}{-4} ina he tango te ±. Tango 6 mai i -26.

$$x=-\frac{32}{-4}$$

Whakawehe -32 ki te -4.

$$x=8$$

Kua oti te whārite te whakatau.

$$x=5 x=8$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 25 ki te 1, ka 26.

$$\left(26-2x\right)x=80$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26-2x ki te x.

$$26x-2x^{2}=80$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-2x^{2}+26x=80$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+26x}{-2}=\frac{80}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\frac{26}{-2}x=\frac{80}{-2}$$

Whakawehe 26 ki te -2.

$$x^{2}-13x=\frac{80}{-2}$$

Whakawehe 80 ki te -2.

$$x^{2}-13x=-40$$

Whakawehea te -13, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{2}. Nā, tāpiria te pūrua o te -\frac{13}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-13x+\left(-\frac{13}{2}\right)^{2}=-40+\left(-\frac{13}{2}\right)^{2}$$

Pūruatia -\frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-13x+\frac{169}{4}=-40+\frac{169}{4}$$

Tāpiri -40 ki te \frac{169}{4}.

$$x^{2}-13x+\frac{169}{4}=\frac{9}{4}$$

Tauwehea x^{2}-13x+\frac{169}{4}. 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}.

$$\left(x-\frac{13}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{13}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x-\frac{13}{2}=\frac{3}{2} x-\frac{13}{2}=-\frac{3}{2}$$

Me tāpiri \frac{13}{2} ki ngā taha e rua o te whārite.

$$x=8 x=5$$