Whakaoti i te (x+10)(2x-3)=54

$$(x+10)(2x-3)=54$$

Whakaoti mō x

$$x=-12$$

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+10 ki te 2x-3 ka whakakotahi i ngā kupu rite.

$$2x^{2}+17x-30=54$$

Tangohia te 54 mai i ngā taha e rua.

$$2x^{2}+17x-30-54=0$$

Tangohia te 54 i te -30, ka -84.

$$2x^{2}+17x-84=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 17 mō b, me -84 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\times 2\left(-84\right)}}{2\times 2}$$

Pūrua 17.

$$x=\frac{-17±\sqrt{289-4\times 2\left(-84\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-17±\sqrt{289-8\left(-84\right)}}{2\times 2}$$

Whakareatia -8 ki te -84.

$$x=\frac{-17±\sqrt{289+672}}{2\times 2}$$

Tāpiri 289 ki te 672.

$$x=\frac{-17±\sqrt{961}}{2\times 2}$$

Tuhia te pūtakerua o te 961.

$$x=\frac{-17±31}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-17±31}{4}$$

Nā, me whakaoti te whārite x=\frac{-17±31}{4} ina he tāpiri te ±. Tāpiri -17 ki te 31.

$$x=\frac{14}{4}$$

Whakahekea te hautanga \frac{14}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Nā, me whakaoti te whārite x=\frac{-17±31}{4} ina he tango te ±. Tango 31 mai i -17.

$$x=-\frac{48}{4}$$

Whakawehe -48 ki te 4.

$$x=-12$$

Kua oti te whārite te whakatau.

$$x=\frac{7}{2} x=-12$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+10 ki te 2x-3 ka whakakotahi i ngā kupu rite.

$$2x^{2}+17x-30=54$$

Me tāpiri te 30 ki ngā taha e rua.

$$2x^{2}+17x=54+30$$

Tāpirihia te 54 ki te 30, ka 84.

$$2x^{2}+17x=84$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+17x}{2}=\frac{84}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{17}{2}x=\frac{84}{2}$$

Whakawehe 84 ki te 2.

$$x^{2}+\frac{17}{2}x=42$$

Whakawehea te \frac{17}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{17}{4}. Nā, tāpiria te pūrua o te \frac{17}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{17}{2}x+\left(\frac{17}{4}\right)^{2}=42+\left(\frac{17}{4}\right)^{2}$$

Pūruatia \frac{17}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{17}{2}x+\frac{289}{16}=42+\frac{289}{16}$$

Tāpiri 42 ki te \frac{289}{16}.

$$x^{2}+\frac{17}{2}x+\frac{289}{16}=\frac{961}{16}$$

Tauwehea x^{2}+\frac{17}{2}x+\frac{289}{16}. 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}.

$$\left(x+\frac{17}{4}\right)^{2}=\frac{961}{16}$$

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

$$\sqrt{\left(x+\frac{17}{4}\right)^{2}}=\sqrt{\frac{961}{16}}$$

Whakarūnātia.

$$x+\frac{17}{4}=\frac{31}{4} x+\frac{17}{4}=-\frac{31}{4}$$

Me tango \frac{17}{4} mai i ngā taha e rua o te whārite.

$$x=\frac{7}{2} x=-12$$