Whakaoti i te 78/x+8*7=2x

$$7 \frac{ 8 }{ x } +8 \cdot 7 = 2x$$

Whakaoti mō x

$$x=4\sqrt{14}+14\approx 28.966629547$$

$$x=14-4\sqrt{14}\approx -0.966629547$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$7\times 8+8\times 7x=2xx$$

Whakareatia te x ki te x, ka x^{2}.

$$7\times 8+8\times 7x=2x^{2}$$

Whakareatia te 7 ki te 8, ka 56. Whakareatia te 8 ki te 7, ka 56.

$$56+56x=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$56+56x-2x^{2}=0$$

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.

$$-2x^{2}+56x+56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 56 mō b, me 56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-56±\sqrt{56^{2}-4\left(-2\right)\times 56}}{2\left(-2\right)}$$

Pūrua 56.

$$x=\frac{-56±\sqrt{3136-4\left(-2\right)\times 56}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-56±\sqrt{3136+8\times 56}}{2\left(-2\right)}$$

Whakareatia 8 ki te 56.

$$x=\frac{-56±\sqrt{3136+448}}{2\left(-2\right)}$$

Tāpiri 3136 ki te 448.

$$x=\frac{-56±\sqrt{3584}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 3584.

$$x=\frac{-56±16\sqrt{14}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-56±16\sqrt{14}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-56±16\sqrt{14}}{-4} ina he tāpiri te ±. Tāpiri -56 ki te 16\sqrt{14}.

$$x=\frac{16\sqrt{14}-56}{-4}$$

Whakawehe -56+16\sqrt{14} ki te -4.

$$x=14-4\sqrt{14}$$

Nā, me whakaoti te whārite x=\frac{-56±16\sqrt{14}}{-4} ina he tango te ±. Tango 16\sqrt{14} mai i -56.

$$x=\frac{-16\sqrt{14}-56}{-4}$$

Whakawehe -56-16\sqrt{14} ki te -4.

$$x=4\sqrt{14}+14$$

Kua oti te whārite te whakatau.

$$x=14-4\sqrt{14} x=4\sqrt{14}+14$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$7\times 8+8\times 7x=2xx$$

Whakareatia te x ki te x, ka x^{2}.

$$7\times 8+8\times 7x=2x^{2}$$

Whakareatia te 7 ki te 8, ka 56. Whakareatia te 8 ki te 7, ka 56.

$$56+56x=2x^{2}$$

Tangohia te 2x^{2} mai i ngā taha e rua.

$$56+56x-2x^{2}=0$$

Tangohia te 56 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$56x-2x^{2}=-56$$

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.

$$-2x^{2}+56x=-56$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+56x}{-2}=-\frac{56}{-2}$$

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

$$x^{2}+\frac{56}{-2}x=-\frac{56}{-2}$$

Whakawehe 56 ki te -2.

$$x^{2}-28x=-\frac{56}{-2}$$

Whakawehe -56 ki te -2.

$$x^{2}-28x=28$$

Whakawehea te -28, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -14. Nā, tāpiria te pūrua o te -14 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-28x+\left(-14\right)^{2}=28+\left(-14\right)^{2}$$

Pūrua -14.

$$x^{2}-28x+196=28+196$$

Tāpiri 28 ki te 196.

$$x^{2}-28x+196=224$$

Tauwehea x^{2}-28x+196. 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}.

$$\left(x-14\right)^{2}=224$$

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

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{224}$$

Whakarūnātia.

$$x-14=4\sqrt{14} x-14=-4\sqrt{14}$$

Me tāpiri 14 ki ngā taha e rua o te whārite.

$$x=4\sqrt{14}+14 x=14-4\sqrt{14}$$