Whakaoti i te 8x^2-5x+87=7x^2+5x

$$8 x ^ { 2 } - 5 x + 87 = 7 x ^ { 2 } + 5 x$$

Whakaoti mō x (complex solution)

$$x=5+\sqrt{62}i\approx 5+7.874007874i$$

$$x=-\sqrt{62}i+5\approx 5-7.874007874i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7x^{2} mai i ngā taha e rua.

$$8x^{2}-5x+87-7x^{2}=5x$$

Pahekotia te 8x^{2} me -7x^{2}, ka x^{2}.

$$x^{2}-5x+87=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$x^{2}-5x+87-5x=0$$

Pahekotia te -5x me -5x, ka -10x.

$$x^{2}-10x+87=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me 87 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 87}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 87}}{2}$$

Whakareatia -4 ki te 87.

$$x=\frac{-\left(-10\right)±\sqrt{100-348}}{2}$$

Tāpiri 100 ki te -348.

$$x=\frac{-\left(-10\right)±\sqrt{-248}}{2}$$

Tuhia te pūtakerua o te -248.

$$x=\frac{-\left(-10\right)±2\sqrt{62}i}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{62}i}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{62}i}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2i\sqrt{62}.

$$x=\frac{10+2\sqrt{62}i}{2}$$

Whakawehe 10+2i\sqrt{62} ki te 2.

$$x=5+\sqrt{62}i$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{62}i}{2} ina he tango te ±. Tango 2i\sqrt{62} mai i 10.

$$x=\frac{-2\sqrt{62}i+10}{2}$$

Whakawehe 10-2i\sqrt{62} ki te 2.

$$x=-\sqrt{62}i+5$$

Kua oti te whārite te whakatau.

$$x=5+\sqrt{62}i x=-\sqrt{62}i+5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 7x^{2} mai i ngā taha e rua.

$$8x^{2}-5x+87-7x^{2}=5x$$

Pahekotia te 8x^{2} me -7x^{2}, ka x^{2}.

$$x^{2}-5x+87=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$x^{2}-5x+87-5x=0$$

Pahekotia te -5x me -5x, ka -10x.

$$x^{2}-10x+87=0$$

Tangohia te 87 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-10x=-87$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-10x+\left(-5\right)^{2}=-87+\left(-5\right)^{2}$$

Pūrua -5.

$$x^{2}-10x+25=-87+25$$

Tāpiri -87 ki te 25.

$$x^{2}-10x+25=-62$$

Tauwehea x^{2}-10x+25. 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}.

$$\left(x-5\right)^{2}=-62$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{-62}$$

Whakarūnātia.

$$x-5=\sqrt{62}i x-5=-\sqrt{62}i$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=5+\sqrt{62}i x=-\sqrt{62}i+5$$