Whakaoti i te (2x+2)(x+3)=96

$$( 2 x + 2 ) ( x + 3 ) = 96$$

Whakaoti mō x

$$x=-9$$

$$x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$2x^{2}+8x+6=96$$

Tangohia te 96 mai i ngā taha e rua.

$$2x^{2}+8x+6-96=0$$

Tangohia te 96 i te 6, ka -90.

$$2x^{2}+8x-90=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 8 mō b, me -90 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2\left(-90\right)}}{2\times 2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 2\left(-90\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-8±\sqrt{64-8\left(-90\right)}}{2\times 2}$$

Whakareatia -8 ki te -90.

$$x=\frac{-8±\sqrt{64+720}}{2\times 2}$$

Tāpiri 64 ki te 720.

$$x=\frac{-8±\sqrt{784}}{2\times 2}$$

Tuhia te pūtakerua o te 784.

$$x=\frac{-8±28}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-8±28}{4}$$

Nā, me whakaoti te whārite x=\frac{-8±28}{4} ina he tāpiri te ±. Tāpiri -8 ki te 28.

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

Whakawehe 20 ki te 4.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{-8±28}{4} ina he tango te ±. Tango 28 mai i -8.

$$x=-\frac{36}{4}$$

Whakawehe -36 ki te 4.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=5 x=-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$2x^{2}+8x+6=96$$

Tangohia te 6 mai i ngā taha e rua.

$$2x^{2}+8x=96-6$$

Tangohia te 6 i te 96, ka 90.

$$2x^{2}+8x=90$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+8x}{2}=\frac{90}{2}$$

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

$$x^{2}+\frac{8}{2}x=\frac{90}{2}$$

Whakawehe 8 ki te 2.

$$x^{2}+4x=\frac{90}{2}$$

Whakawehe 90 ki te 2.

$$x^{2}+4x=45$$

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.

$$x^{2}+4x+2^{2}=45+2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=45+4$$

Tāpiri 45 ki te 4.

$$x^{2}+4x+4=49$$

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}.

$$\left(x+2\right)^{2}=49$$

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{49}$$

Whakarūnātia.

$$x+2=7 x+2=-7$$

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

$$x=5 x=-9$$