Whakaoti i te (x-35)*(x+38-25)=253575

$$(x-35) \times (x+38-25)=253575$$

Whakaoti mō x

$$x=3\sqrt{28239}+11\approx 515.133910782$$

$$x=11-3\sqrt{28239}\approx -493.133910782$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 25 i te 38, ka 13.

$$\left(x-35\right)\left(x+13\right)=253575$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-35 ki te x+13 ka whakakotahi i ngā kupu rite.

$$x^{2}-22x-455=253575$$

Tangohia te 253575 mai i ngā taha e rua.

$$x^{2}-22x-455-253575=0$$

Tangohia te 253575 i te -455, ka -254030.

$$x^{2}-22x-254030=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -22 mō b, me -254030 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\left(-254030\right)}}{2}$$

Pūrua -22.

$$x=\frac{-\left(-22\right)±\sqrt{484-4\left(-254030\right)}}{2}$$

Whakareatia -4 ki te -254030.

$$x=\frac{-\left(-22\right)±\sqrt{484+1016120}}{2}$$

Tāpiri 484 ki te 1016120.

$$x=\frac{-\left(-22\right)±\sqrt{1016604}}{2}$$

Tuhia te pūtakerua o te 1016604.

$$x=\frac{-\left(-22\right)±6\sqrt{28239}}{2}$$

Ko te tauaro o -22 ko 22.

$$x=\frac{22±6\sqrt{28239}}{2}$$

Nā, me whakaoti te whārite x=\frac{22±6\sqrt{28239}}{2} ina he tāpiri te ±. Tāpiri 22 ki te 6\sqrt{28239}.

$$x=\frac{6\sqrt{28239}+22}{2}$$

Whakawehe 22+6\sqrt{28239} ki te 2.

$$x=3\sqrt{28239}+11$$

Nā, me whakaoti te whārite x=\frac{22±6\sqrt{28239}}{2} ina he tango te ±. Tango 6\sqrt{28239} mai i 22.

$$x=\frac{22-6\sqrt{28239}}{2}$$

Whakawehe 22-6\sqrt{28239} ki te 2.

$$x=11-3\sqrt{28239}$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{28239}+11 x=11-3\sqrt{28239}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 25 i te 38, ka 13.

$$\left(x-35\right)\left(x+13\right)=253575$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-35 ki te x+13 ka whakakotahi i ngā kupu rite.

$$x^{2}-22x-455=253575$$

Me tāpiri te 455 ki ngā taha e rua.

$$x^{2}-22x=253575+455$$

Tāpirihia te 253575 ki te 455, ka 254030.

$$x^{2}-22x=254030$$

Whakawehea te -22, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -11. Nā, tāpiria te pūrua o te -11 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-22x+\left(-11\right)^{2}=254030+\left(-11\right)^{2}$$

Pūrua -11.

$$x^{2}-22x+121=254030+121$$

Tāpiri 254030 ki te 121.

$$x^{2}-22x+121=254151$$

Tauwehea x^{2}-22x+121. 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}.

$$\left(x-11\right)^{2}=254151$$

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

$$\sqrt{\left(x-11\right)^{2}}=\sqrt{254151}$$

Whakarūnātia.

$$x-11=3\sqrt{28239} x-11=-3\sqrt{28239}$$

Me tāpiri 11 ki ngā taha e rua o te whārite.

$$x=3\sqrt{28239}+11 x=11-3\sqrt{28239}$$