Whakaoti i te 0.75x^2+15x-727.48=0

$$0.75 { x }^{ 2 } +15x-727.48=0$$

Whakaoti mō x

$$x=\frac{2\sqrt{60186}}{15}-10\approx 22.710446853$$

$$x=-\frac{2\sqrt{60186}}{15}-10\approx -42.710446853$$

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.

$$0.75x^{2}+15x-727.48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.75 mō a, 15 mō b, me -727.48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-15±\sqrt{15^{2}-4\times 0.75\left(-727.48\right)}}{2\times 0.75}$$

Pūrua 15.

$$x=\frac{-15±\sqrt{225-4\times 0.75\left(-727.48\right)}}{2\times 0.75}$$

Whakareatia -4 ki te 0.75.

$$x=\frac{-15±\sqrt{225-3\left(-727.48\right)}}{2\times 0.75}$$

Whakareatia -3 ki te -727.48.

$$x=\frac{-15±\sqrt{225+2182.44}}{2\times 0.75}$$

Tāpiri 225 ki te 2182.44.

$$x=\frac{-15±\sqrt{2407.44}}{2\times 0.75}$$

Tuhia te pūtakerua o te 2407.44.

$$x=\frac{-15±\frac{\sqrt{60186}}{5}}{2\times 0.75}$$

Whakareatia 2 ki te 0.75.

$$x=\frac{-15±\frac{\sqrt{60186}}{5}}{1.5}$$

Nā, me whakaoti te whārite x=\frac{-15±\frac{\sqrt{60186}}{5}}{1.5} ina he tāpiri te ±. Tāpiri -15 ki te \frac{\sqrt{60186}}{5}.

$$x=\frac{\frac{\sqrt{60186}}{5}-15}{1.5}$$

Whakawehe -15+\frac{\sqrt{60186}}{5} ki te 1.5 mā te whakarea -15+\frac{\sqrt{60186}}{5} ki te tau huripoki o 1.5.

$$x=\frac{2\sqrt{60186}}{15}-10$$

Nā, me whakaoti te whārite x=\frac{-15±\frac{\sqrt{60186}}{5}}{1.5} ina he tango te ±. Tango \frac{\sqrt{60186}}{5} mai i -15.

$$x=\frac{-\frac{\sqrt{60186}}{5}-15}{1.5}$$

Whakawehe -15-\frac{\sqrt{60186}}{5} ki te 1.5 mā te whakarea -15-\frac{\sqrt{60186}}{5} ki te tau huripoki o 1.5.

$$x=-\frac{2\sqrt{60186}}{15}-10$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{60186}}{15}-10 x=-\frac{2\sqrt{60186}}{15}-10$$

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.

$$0.75x^{2}+15x-727.48=0$$

Me tāpiri 727.48 ki ngā taha e rua o te whārite.

$$0.75x^{2}+15x-727.48-\left(-727.48\right)=-\left(-727.48\right)$$

Mā te tango i te -727.48 i a ia ake anō ka toe ko te 0.

$$0.75x^{2}+15x=-\left(-727.48\right)$$

Tango -727.48 mai i 0.

$$0.75x^{2}+15x=727.48$$

Whakawehea ngā taha e rua o te whārite ki te 0.75, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{0.75x^{2}+15x}{0.75}=\frac{727.48}{0.75}$$

Mā te whakawehe ki te 0.75 ka wetekia te whakareanga ki te 0.75.

$$x^{2}+\frac{15}{0.75}x=\frac{727.48}{0.75}$$

Whakawehe 15 ki te 0.75 mā te whakarea 15 ki te tau huripoki o 0.75.

$$x^{2}+20x=\frac{727.48}{0.75}$$

Whakawehe 727.48 ki te 0.75 mā te whakarea 727.48 ki te tau huripoki o 0.75.

$$x^{2}+20x=\frac{72748}{75}$$

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.

$$x^{2}+20x+10^{2}=\frac{72748}{75}+10^{2}$$

Pūrua 10.

$$x^{2}+20x+100=\frac{72748}{75}+100$$

Tāpiri \frac{72748}{75} ki te 100.

$$x^{2}+20x+100=\frac{80248}{75}$$

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}.

$$\left(x+10\right)^{2}=\frac{80248}{75}$$

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

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{\frac{80248}{75}}$$

Whakarūnātia.

$$x+10=\frac{2\sqrt{60186}}{15} x+10=-\frac{2\sqrt{60186}}{15}$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{60186}}{15}-10 x=-\frac{2\sqrt{60186}}{15}-10$$