Whakaoti i te 1428=(18+2x)(26+2x)

$$1428 = ( 18 + 2 x ) ( 26 + 2 x )$$

Whakaoti mō x

$$x=-30$$

$$x=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 18+2x ki te 26+2x ka whakakotahi i ngā kupu rite.

$$1428=468+88x+4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$468+88x+4x^{2}=1428$$

Tangohia te 1428 mai i ngā taha e rua.

$$468+88x+4x^{2}-1428=0$$

Tangohia te 1428 i te 468, ka -960.

$$-960+88x+4x^{2}=0$$

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.

$$4x^{2}+88x-960=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 88 mō b, me -960 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-88±\sqrt{88^{2}-4\times 4\left(-960\right)}}{2\times 4}$$

Pūrua 88.

$$x=\frac{-88±\sqrt{7744-4\times 4\left(-960\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-88±\sqrt{7744-16\left(-960\right)}}{2\times 4}$$

Whakareatia -16 ki te -960.

$$x=\frac{-88±\sqrt{7744+15360}}{2\times 4}$$

Tāpiri 7744 ki te 15360.

$$x=\frac{-88±\sqrt{23104}}{2\times 4}$$

Tuhia te pūtakerua o te 23104.

$$x=\frac{-88±152}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-88±152}{8}$$

Nā, me whakaoti te whārite x=\frac{-88±152}{8} ina he tāpiri te ±. Tāpiri -88 ki te 152.

$$x=\frac{64}{8}$$

Whakawehe 64 ki te 8.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{-88±152}{8} ina he tango te ±. Tango 152 mai i -88.

$$x=-\frac{240}{8}$$

Whakawehe -240 ki te 8.

$$x=-30$$

Kua oti te whārite te whakatau.

$$x=8 x=-30$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 18+2x ki te 26+2x ka whakakotahi i ngā kupu rite.

$$1428=468+88x+4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$468+88x+4x^{2}=1428$$

Tangohia te 468 mai i ngā taha e rua.

$$88x+4x^{2}=1428-468$$

Tangohia te 468 i te 1428, ka 960.

$$88x+4x^{2}=960$$

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.

$$4x^{2}+88x=960$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+88x}{4}=\frac{960}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{88}{4}x=\frac{960}{4}$$

Whakawehe 88 ki te 4.

$$x^{2}+22x=\frac{960}{4}$$

Whakawehe 960 ki te 4.

$$x^{2}+22x=240$$

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.

$$x^{2}+22x+11^{2}=240+11^{2}$$

Pūrua 11.

$$x^{2}+22x+121=240+121$$

Tāpiri 240 ki te 121.

$$x^{2}+22x+121=361$$

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}.

$$\left(x+11\right)^{2}=361$$

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

$$\sqrt{\left(x+11\right)^{2}}=\sqrt{361}$$

Whakarūnātia.

$$x+11=19 x+11=-19$$

Me tango 11 mai i ngā taha e rua o te whārite.

$$x=8 x=-30$$