Whakaoti i te (x+10)(x+10)=25

$$( x + 10 ) ( x + 10 ) = 25$$

Whakaoti mō x

$$x=-5$$

$$x=-15$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x+10 ki te x+10, ka \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=25$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+10\right)^{2}.

$$x^{2}+20x+100=25$$

Tangohia te 25 mai i ngā taha e rua.

$$x^{2}+20x+100-25=0$$

Tangohia te 25 i te 100, ka 75.

$$x^{2}+20x+75=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 20 mō b, me 75 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\times 75}}{2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 75}}{2}$$

Whakareatia -4 ki te 75.

$$x=\frac{-20±\sqrt{400-300}}{2}$$

Tāpiri 400 ki te -300.

$$x=\frac{-20±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-20±10}{2}$$

Nā, me whakaoti te whārite x=\frac{-20±10}{2} ina he tāpiri te ±. Tāpiri -20 ki te 10.

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

Whakawehe -10 ki te 2.

$$x=-5$$

Nā, me whakaoti te whārite x=\frac{-20±10}{2} ina he tango te ±. Tango 10 mai i -20.

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

Whakawehe -30 ki te 2.

$$x=-15$$

Kua oti te whārite te whakatau.

$$x=-5 x=-15$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x+10 ki te x+10, ka \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=25$$

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

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$x+10=5 x+10=-5$$

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

$$x=-5 x=-15$$