Whakaoti i te 5062=R(R+200)

$$5062 = R ( R + 200 )$$

Whakaoti mō R

$$R=\sqrt{15062}-100\approx 22.727340067$$

$$R=-\sqrt{15062}-100\approx -222.727340067$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te R ki te R+200.

$$5062=R^{2}+200R$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$R^{2}+200R=5062$$

Tangohia te 5062 mai i ngā taha e rua.

$$R^{2}+200R-5062=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 200 mō b, me -5062 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{-200±\sqrt{200^{2}-4\left(-5062\right)}}{2}$$

Pūrua 200.

$$R=\frac{-200±\sqrt{40000-4\left(-5062\right)}}{2}$$

Whakareatia -4 ki te -5062.

$$R=\frac{-200±\sqrt{40000+20248}}{2}$$

Tāpiri 40000 ki te 20248.

$$R=\frac{-200±\sqrt{60248}}{2}$$

Tuhia te pūtakerua o te 60248.

$$R=\frac{-200±2\sqrt{15062}}{2}$$

Nā, me whakaoti te whārite R=\frac{-200±2\sqrt{15062}}{2} ina he tāpiri te ±. Tāpiri -200 ki te 2\sqrt{15062}.

$$R=\frac{2\sqrt{15062}-200}{2}$$

Whakawehe -200+2\sqrt{15062} ki te 2.

$$R=\sqrt{15062}-100$$

Nā, me whakaoti te whārite R=\frac{-200±2\sqrt{15062}}{2} ina he tango te ±. Tango 2\sqrt{15062} mai i -200.

$$R=\frac{-2\sqrt{15062}-200}{2}$$

Whakawehe -200-2\sqrt{15062} ki te 2.

$$R=-\sqrt{15062}-100$$

Kua oti te whārite te whakatau.

$$R=\sqrt{15062}-100 R=-\sqrt{15062}-100$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te R ki te R+200.

$$5062=R^{2}+200R$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$R^{2}+200R=5062$$

Whakawehea te 200, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 100. Nā, tāpiria te pūrua o te 100 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$R^{2}+200R+100^{2}=5062+100^{2}$$

Pūrua 100.

$$R^{2}+200R+10000=5062+10000$$

Tāpiri 5062 ki te 10000.

$$R^{2}+200R+10000=15062$$

Tauwehea R^{2}+200R+10000. 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}.

$$\left(R+100\right)^{2}=15062$$

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

$$\sqrt{\left(R+100\right)^{2}}=\sqrt{15062}$$

Whakarūnātia.

$$R+100=\sqrt{15062} R+100=-\sqrt{15062}$$

Me tango 100 mai i ngā taha e rua o te whārite.

$$R=\sqrt{15062}-100 R=-\sqrt{15062}-100$$