Whakaoti i te (11x+4)(11x+40)=1612

$$(11x+4)(11x+40)=1612$$

Whakaoti mō x

$$x=-6$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 11x+4 ki te 11x+40 ka whakakotahi i ngā kupu rite.

$$121x^{2}+484x+160=1612$$

Tangohia te 1612 mai i ngā taha e rua.

$$121x^{2}+484x+160-1612=0$$

Tangohia te 1612 i te 160, ka -1452.

$$121x^{2}+484x-1452=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 121 mō a, 484 mō b, me -1452 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-484±\sqrt{484^{2}-4\times 121\left(-1452\right)}}{2\times 121}$$

Pūrua 484.

$$x=\frac{-484±\sqrt{234256-4\times 121\left(-1452\right)}}{2\times 121}$$

Whakareatia -4 ki te 121.

$$x=\frac{-484±\sqrt{234256-484\left(-1452\right)}}{2\times 121}$$

Whakareatia -484 ki te -1452.

$$x=\frac{-484±\sqrt{234256+702768}}{2\times 121}$$

Tāpiri 234256 ki te 702768.

$$x=\frac{-484±\sqrt{937024}}{2\times 121}$$

Tuhia te pūtakerua o te 937024.

$$x=\frac{-484±968}{2\times 121}$$

Whakareatia 2 ki te 121.

$$x=\frac{-484±968}{242}$$

Nā, me whakaoti te whārite x=\frac{-484±968}{242} ina he tāpiri te ±. Tāpiri -484 ki te 968.

$$x=\frac{484}{242}$$

Whakawehe 484 ki te 242.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{-484±968}{242} ina he tango te ±. Tango 968 mai i -484.

$$x=-\frac{1452}{242}$$

Whakawehe -1452 ki te 242.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=2 x=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 11x+4 ki te 11x+40 ka whakakotahi i ngā kupu rite.

$$121x^{2}+484x+160=1612$$

Tangohia te 160 mai i ngā taha e rua.

$$121x^{2}+484x=1612-160$$

Tangohia te 160 i te 1612, ka 1452.

$$121x^{2}+484x=1452$$

Whakawehea ngā taha e rua ki te 121.

$$\frac{121x^{2}+484x}{121}=\frac{1452}{121}$$

Mā te whakawehe ki te 121 ka wetekia te whakareanga ki te 121.

$$x^{2}+\frac{484}{121}x=\frac{1452}{121}$$

Whakawehe 484 ki te 121.

$$x^{2}+4x=\frac{1452}{121}$$

Whakawehe 1452 ki te 121.

$$x^{2}+4x=12$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+4x+2^{2}=12+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=12+4$$

Tāpiri 12 ki te 4.

$$x^{2}+4x+4=16$$

Tauwehea x^{2}+4x+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}.

$$\left(x+2\right)^{2}=16$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$x+2=4 x+2=-4$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=2 x=-6$$