Whakaoti i te (100+2x)(60+2x)=200*60

$$( 100 + 2 x ) ( 60 + 2 x ) = 200 \times 60$$

Whakaoti mō x

$$x=10\sqrt{31}-40\approx 15.677643628$$

$$x=-10\sqrt{31}-40\approx -95.677643628$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 100+2x ki te 60+2x ka whakakotahi i ngā kupu rite.

$$6000+320x+4x^{2}=200\times 60$$

Whakareatia te 200 ki te 60, ka 12000.

$$6000+320x+4x^{2}=12000$$

Tangohia te 12000 mai i ngā taha e rua.

$$6000+320x+4x^{2}-12000=0$$

Tangohia te 12000 i te 6000, ka -6000.

$$-6000+320x+4x^{2}=0$$

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.

$$4x^{2}+320x-6000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 320 mō b, me -6000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-320±\sqrt{320^{2}-4\times 4\left(-6000\right)}}{2\times 4}$$

Pūrua 320.

$$x=\frac{-320±\sqrt{102400-4\times 4\left(-6000\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-320±\sqrt{102400-16\left(-6000\right)}}{2\times 4}$$

Whakareatia -16 ki te -6000.

$$x=\frac{-320±\sqrt{102400+96000}}{2\times 4}$$

Tāpiri 102400 ki te 96000.

$$x=\frac{-320±\sqrt{198400}}{2\times 4}$$

Tuhia te pūtakerua o te 198400.

$$x=\frac{-320±80\sqrt{31}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-320±80\sqrt{31}}{8}$$

Nā, me whakaoti te whārite x=\frac{-320±80\sqrt{31}}{8} ina he tāpiri te ±. Tāpiri -320 ki te 80\sqrt{31}.

$$x=\frac{80\sqrt{31}-320}{8}$$

Whakawehe -320+80\sqrt{31} ki te 8.

$$x=10\sqrt{31}-40$$

Nā, me whakaoti te whārite x=\frac{-320±80\sqrt{31}}{8} ina he tango te ±. Tango 80\sqrt{31} mai i -320.

$$x=\frac{-80\sqrt{31}-320}{8}$$

Whakawehe -320-80\sqrt{31} ki te 8.

$$x=-10\sqrt{31}-40$$

Kua oti te whārite te whakatau.

$$x=10\sqrt{31}-40 x=-10\sqrt{31}-40$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 100+2x ki te 60+2x ka whakakotahi i ngā kupu rite.

$$6000+320x+4x^{2}=200\times 60$$

Whakareatia te 200 ki te 60, ka 12000.

$$6000+320x+4x^{2}=12000$$

Tangohia te 6000 mai i ngā taha e rua.

$$320x+4x^{2}=12000-6000$$

Tangohia te 6000 i te 12000, ka 6000.

$$320x+4x^{2}=6000$$

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.

$$4x^{2}+320x=6000$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+320x}{4}=\frac{6000}{4}$$

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

$$x^{2}+\frac{320}{4}x=\frac{6000}{4}$$

Whakawehe 320 ki te 4.

$$x^{2}+80x=\frac{6000}{4}$$

Whakawehe 6000 ki te 4.

$$x^{2}+80x=1500$$

Whakawehea te 80, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 40. Nā, tāpiria te pūrua o te 40 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+80x+40^{2}=1500+40^{2}$$

Pūrua 40.

$$x^{2}+80x+1600=1500+1600$$

Tāpiri 1500 ki te 1600.

$$x^{2}+80x+1600=3100$$

Tauwehea x^{2}+80x+1600. 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}.

$$\left(x+40\right)^{2}=3100$$

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

$$\sqrt{\left(x+40\right)^{2}}=\sqrt{3100}$$

Whakarūnātia.

$$x+40=10\sqrt{31} x+40=-10\sqrt{31}$$

Me tango 40 mai i ngā taha e rua o te whārite.

$$x=10\sqrt{31}-40 x=-10\sqrt{31}-40$$