Whakaoti i te 5x*10-9xdiv2x=99

$$5x \times 10-9x \div 2x=99$$

Whakaoti mō x

$$x = \frac{\sqrt{718} + 50}{9} \approx 8.532835779$$

$$x = \frac{50 - \sqrt{718}}{9} \approx 2.578275332$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$10x\times 10-9xx=198$$

Whakareatia te 10 ki te 10, ka 100.

$$100x-9xx=198$$

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

$$100x-9x^{2}=198$$

Tangohia te 198 mai i ngā taha e rua.

$$100x-9x^{2}-198=0$$

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.

$$-9x^{2}+100x-198=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -9 mō a, 100 mō b, me -198 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-9\right)\left(-198\right)}}{2\left(-9\right)}$$

Pūrua 100.

$$x=\frac{-100±\sqrt{10000-4\left(-9\right)\left(-198\right)}}{2\left(-9\right)}$$

Whakareatia -4 ki te -9.

$$x=\frac{-100±\sqrt{10000+36\left(-198\right)}}{2\left(-9\right)}$$

Whakareatia 36 ki te -198.

$$x=\frac{-100±\sqrt{10000-7128}}{2\left(-9\right)}$$

Tāpiri 10000 ki te -7128.

$$x=\frac{-100±\sqrt{2872}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 2872.

$$x=\frac{-100±2\sqrt{718}}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$x=\frac{-100±2\sqrt{718}}{-18}$$

Nā, me whakaoti te whārite x=\frac{-100±2\sqrt{718}}{-18} ina he tāpiri te ±. Tāpiri -100 ki te 2\sqrt{718}.

$$x=\frac{2\sqrt{718}-100}{-18}$$

Whakawehe -100+2\sqrt{718} ki te -18.

$$x=\frac{50-\sqrt{718}}{9}$$

Nā, me whakaoti te whārite x=\frac{-100±2\sqrt{718}}{-18} ina he tango te ±. Tango 2\sqrt{718} mai i -100.

$$x=\frac{-2\sqrt{718}-100}{-18}$$

Whakawehe -100-2\sqrt{718} ki te -18.

$$x=\frac{\sqrt{718}+50}{9}$$

Kua oti te whārite te whakatau.

$$x=\frac{50-\sqrt{718}}{9} x=\frac{\sqrt{718}+50}{9}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$10x\times 10-9xx=198$$

Whakareatia te 10 ki te 10, ka 100.

$$100x-9xx=198$$

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

$$100x-9x^{2}=198$$

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.

$$-9x^{2}+100x=198$$

Whakawehea ngā taha e rua ki te -9.

$$\frac{-9x^{2}+100x}{-9}=\frac{198}{-9}$$

Mā te whakawehe ki te -9 ka wetekia te whakareanga ki te -9.

$$x^{2}+\frac{100}{-9}x=\frac{198}{-9}$$

Whakawehe 100 ki te -9.

$$x^{2}-\frac{100}{9}x=\frac{198}{-9}$$

Whakawehe 198 ki te -9.

$$x^{2}-\frac{100}{9}x=-22$$

Whakawehea te -\frac{100}{9}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{50}{9}. Nā, tāpiria te pūrua o te -\frac{50}{9} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{100}{9}x+\left(-\frac{50}{9}\right)^{2}=-22+\left(-\frac{50}{9}\right)^{2}$$

Pūruatia -\frac{50}{9} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{100}{9}x+\frac{2500}{81}=-22+\frac{2500}{81}$$

Tāpiri -22 ki te \frac{2500}{81}.

$$x^{2}-\frac{100}{9}x+\frac{2500}{81}=\frac{718}{81}$$

Tauwehea x^{2}-\frac{100}{9}x+\frac{2500}{81}. 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}.

$$\left(x-\frac{50}{9}\right)^{2}=\frac{718}{81}$$

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

$$\sqrt{\left(x-\frac{50}{9}\right)^{2}}=\sqrt{\frac{718}{81}}$$

Whakarūnātia.

$$x-\frac{50}{9}=\frac{\sqrt{718}}{9} x-\frac{50}{9}=-\frac{\sqrt{718}}{9}$$

Me tāpiri \frac{50}{9} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{718}+50}{9} x=\frac{50-\sqrt{718}}{9}$$