Whakaoti i te (x-5)(x+1)=-3(5-x)

$$( x - 5 ) ( x + 1 ) = - 3 ( 5 - x )$$

Whakaoti mō x

$$x=2$$

$$x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-5 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}-4x-5=-3\left(5-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 5-x.

$$x^{2}-4x-5=-15+3x$$

Tangohia te -15 mai i ngā taha e rua.

$$x^{2}-4x-5-\left(-15\right)=3x$$

Ko te tauaro o -15 ko 15.

$$x^{2}-4x-5+15=3x$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-4x-5+15-3x=0$$

Tāpirihia te -5 ki te 15, ka 10.

$$x^{2}-4x+10-3x=0$$

Pahekotia te -4x me -3x, ka -7x.

$$x^{2}-7x+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -7 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 10}}{2}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-7\right)±\sqrt{49-40}}{2}$$

Tāpiri 49 ki te -40.

$$x=\frac{-\left(-7\right)±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-\left(-7\right)±3}{2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±3}{2}$$

Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tāpiri te ±. Tāpiri 7 ki te 3.

$$x=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tango te ±. Tango 3 mai i 7.

$$x=\frac{4}{2}$$

Whakawehe 4 ki te 2.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=5 x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-5 ki te x+1 ka whakakotahi i ngā kupu rite.

$$x^{2}-4x-5=-3\left(5-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -3 ki te 5-x.

$$x^{2}-4x-5=-15+3x$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-4x-5-3x=-15$$

Pahekotia te -4x me -3x, ka -7x.

$$x^{2}-7x-5=-15$$

Me tāpiri te 5 ki ngā taha e rua.

$$x^{2}-7x=-15+5$$

Tāpirihia te -15 ki te 5, ka -10.

$$x^{2}-7x=-10$$

Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=-10+\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-7x+\frac{49}{4}=-10+\frac{49}{4}$$

Tāpiri -10 ki te \frac{49}{4}.

$$x^{2}-7x+\frac{49}{4}=\frac{9}{4}$$

Tauwehea x^{2}-7x+\frac{49}{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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{3}{2} x-\frac{7}{2}=-\frac{3}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=5 x=2$$