Whakaoti i te 0.25x^2-5x+8=0

$$0.25 { x }^{ 2 } -5x+8=0$$

Whakaoti mō x

$$x=2\sqrt{17}+10\approx 18.246211251$$

$$x=10-2\sqrt{17}\approx 1.753788749$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$0.25x^{2}-5x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.25 mō a, -5 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 0.25\times 8}}{2\times 0.25}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 0.25\times 8}}{2\times 0.25}$$

Whakareatia -4 ki te 0.25.

$$x=\frac{-\left(-5\right)±\sqrt{25-8}}{2\times 0.25}$$

Tāpiri 25 ki te -8.

$$x=\frac{-\left(-5\right)±\sqrt{17}}{2\times 0.25}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\sqrt{17}}{2\times 0.25}$$

Whakareatia 2 ki te 0.25.

$$x=\frac{5±\sqrt{17}}{0.5}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{17}}{0.5} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{17}.

$$x=\frac{\sqrt{17}+5}{0.5}$$

Whakawehe 5+\sqrt{17} ki te 0.5 mā te whakarea 5+\sqrt{17} ki te tau huripoki o 0.5.

$$x=2\sqrt{17}+10$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{17}}{0.5} ina he tango te ±. Tango \sqrt{17} mai i 5.

$$x=\frac{5-\sqrt{17}}{0.5}$$

Whakawehe 5-\sqrt{17} ki te 0.5 mā te whakarea 5-\sqrt{17} ki te tau huripoki o 0.5.

$$x=10-2\sqrt{17}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{17}+10 x=10-2\sqrt{17}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$0.25x^{2}-5x+8=0$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$0.25x^{2}-5x+8-8=-8$$

Mā te tango i te 8 i a ia ake anō ka toe ko te 0.

$$0.25x^{2}-5x=-8$$

Me whakarea ngā taha e rua ki te 4.

$$\frac{0.25x^{2}-5x}{0.25}=-\frac{8}{0.25}$$

Mā te whakawehe ki te 0.25 ka wetekia te whakareanga ki te 0.25.

$$x^{2}+\left(-\frac{5}{0.25}\right)x=-\frac{8}{0.25}$$

Whakawehe -5 ki te 0.25 mā te whakarea -5 ki te tau huripoki o 0.25.

$$x^{2}-20x=-\frac{8}{0.25}$$

Whakawehe -8 ki te 0.25 mā te whakarea -8 ki te tau huripoki o 0.25.

$$x^{2}-20x=-32$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-20x+\left(-10\right)^{2}=-32+\left(-10\right)^{2}$$

Pūrua -10.

$$x^{2}-20x+100=-32+100$$

Tāpiri -32 ki te 100.

$$x^{2}-20x+100=68$$

Tauwehea x^{2}-20x+100. 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}.

$$\left(x-10\right)^{2}=68$$

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

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{68}$$

Whakarūnātia.

$$x-10=2\sqrt{17} x-10=-2\sqrt{17}$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x=2\sqrt{17}+10 x=10-2\sqrt{17}$$