Whakaoti i te x*(x+5)=300

$$x \times (x+5)=300$$

Whakaoti mō x

$$x=-20$$

$$x=15$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+5.

$$x^{2}+5x=300$$

Tangohia te 300 mai i ngā taha e rua.

$$x^{2}+5x-300=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -300 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-300\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-300\right)}}{2}$$

Whakareatia -4 ki te -300.

$$x=\frac{-5±\sqrt{25+1200}}{2}$$

Tāpiri 25 ki te 1200.

$$x=\frac{-5±\sqrt{1225}}{2}$$

Tuhia te pūtakerua o te 1225.

$$x=\frac{-5±35}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±35}{2} ina he tāpiri te ±. Tāpiri -5 ki te 35.

$$x=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$x=15$$

Nā, me whakaoti te whārite x=\frac{-5±35}{2} ina he tango te ±. Tango 35 mai i -5.

$$x=-\frac{40}{2}$$

Whakawehe -40 ki te 2.

$$x=-20$$

Kua oti te whārite te whakatau.

$$x=15 x=-20$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+5.

$$x^{2}+5x=300$$

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

$$x^{2}+5x+\left(\frac{5}{2}\right)^{2}=300+\left(\frac{5}{2}\right)^{2}$$

Pūruatia \frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+5x+\frac{25}{4}=300+\frac{25}{4}$$

Tāpiri 300 ki te \frac{25}{4}.

$$x^{2}+5x+\frac{25}{4}=\frac{1225}{4}$$

Tauwehea x^{2}+5x+\frac{25}{4}. 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}.

$$\left(x+\frac{5}{2}\right)^{2}=\frac{1225}{4}$$

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

$$\sqrt{\left(x+\frac{5}{2}\right)^{2}}=\sqrt{\frac{1225}{4}}$$

Whakarūnātia.

$$x+\frac{5}{2}=\frac{35}{2} x+\frac{5}{2}=-\frac{35}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$x=15 x=-20$$